[table]capposition=top [figure]capposition=top

Net Buying Pressure and the Information in Bitcoin Option Trades

Carol Alexander,∗∗ Jun Deng,∗ Jianfen Feng,∗ and Huning Wan∗

This Version:

###### Abstract

How do supply and demand from informed traders drive market prices of bitcoin
options? Deribit options tick-level data supports the limits-to-arbitrage
hypothesis about the market maker’s supply. The main demand-side effects are
that at-the-money option prices are largely driven by volatility traders and
out-of-the-money options are simultaneously driven by volatility traders and
those with proprietary information about the direction of future bitcoin price
movements. The demand-side trading results contrast with prior studies on
established options markets in the US and Asia, but we also show that Deribit
is rapidly evolving into a more efficient channel for aggregating information
from informed traders.

Keywords: Deribit options; Informed traders; Market makers; Volatility
information; Directional information;

JEL Classification: G32; G11

** Corresponding author. University of Sussex Business School and Peking
University HSBC Business School. Jubilee Building, University of Sussex,
Falmer, Brighton, BN1 9RH, UK.
<EMAIL_ADDRESS>

* School of Banking and Finance, University of International Business and Economics. No.10, Huixin Dongjie, Chaoyang District, Beijing, 100029, China.
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>
##  1 Introduction

Bitcoin options markets are attracting a growing number of sophisticated and
informed traders. Well-known asset managers such as XBTO have been making
markets in bitcoin options for many years, particularly on the Deribit
exchange, which is much the largest of the popular but self-regulated crypto
options trading platforms with over one billion USD daily trading
volume.111See the websites of XBTO and Deribit. Also, several large
institutions have recently launched managed bitcoin funds that plan to charge
high fees in return for active strategies such as market timing and strategic
hedging using bitcoin options.222See, for example, JP Morgan, CoinDesk, 26
April 2021. It is therefore important for regulators, and for the growing
crypto investment community, to understand the information drivers of bitcoin
option prices. Our study aims to fill this important gap in the literature.

A primary role for financial markets is to aggregate and process information
across different trading venues and to disperse it between market
participants. If bitcoin options market could aggregate and process volatility
and directional information effectively, the regulators and traders would
trust that the market attracts more sophisticated participants and is
functioning well. The information is revealed through trades and prices that
are shaped by the micro-structure of the market and different types of
professional traders, including liquidity providers, arbitragers and brokers.
The fundamental value (if any) and market micro-structure of the Blockchain
based cryptocurrency are quite different from traditional stock and index
markets. The classic work by Easley et al., (1998) shows that two important
determinants of informed trading are the market depth and the potential
leverage available on the platform. Since then, the effect of such trading on
prices and information flows has attracted wide-spread academic interest
focusing on options markets, which allow for particularly fluid information
channels because of the high leverage, low transaction costs and the absence
of short‐selling restrictions. Bitcoin option market makers and traders would
benefit from knowing the mainly driving force for different moneyness options
that helps them to manage inventory and place orders.

A widely-observed phenomenon in options markets is the smile or skew shape of
a fixed-maturity implied volatility curve as a function of the moneyness (or
strike) of the options. Following pioneering work on US markets by Bollen and
Whaley, (2004), it is possible to infer which types of informed traders are
dominating in an options market by relating the observed movements in the
implied volatility smile to a metric called net buying pressure, defined as a
delta-weighted difference between buyer-initiated and seller-initiated option
trades. If the options markets were frictionless and complete, professional
arbitrageurs could hedge positions perfectly and so the market maker’s supply
curves should be independent of the quantity traded. In this case movements in
the implied volatility smile surface should be unrelated to the demand for
options. However, in reality there are many restrictions that prevent perfect
hedging. The costs of hedging increase with the imbalance of a market maker’s
net positions, and so does liquidity risk. To cover these costs and risks they
are forced to charge a risk premium. In other words, the market maker’s
options supply curves slope upwards. The limits-to-arbitrage hypothesis
assumes the market maker would manage inventory at a rational level, so
changes in net demand would affect option prices and hence also their implied
volatilities. In particular, if at any given moneyness level the net buying
pressure is positive (negative), the corresponding implied volatilities would
rise (fall). Under this hypothesis, when changes in implied volatility are
induced by excessive buying pressures in demand, these would reverse when the
market maker rebalances his portfolio.

Bollen and Whaley, (2004) suggest an alternative learning hypothesis whereby
the market maker learns about underlying price dynamics from the trading
activity of traders, and he uses this knowledge to update prices. This way,
implied volatility dynamics will respond to changes in demand from informed
option traders. In this first volatility learning version of the learning
hypothesis, traders are only assumed to trade on their knowledge about
volatility, not the direction of change in the underlying asset price. This
assumption rests on the observation that transaction costs are much higher in
options than they are in spot and futures markets, so directional information
is easier to exploit by trading in spot and futures than it is by trading in
options. However, volatility can only be traded in options markets, using
strategies like butterfly spreads, straddles or strangles.

Regression models devised by Bollen and Whaley, (2004) test for both limits-
to-arbitrage and volatility/directional learning using regressions of implied
volatility changes on different measures of net buying pressure and lagged
changes in implied volatility, controlling for well-known features such as
leverage effects that are independent of either hypothesis. Changes in implied
volatility should be negatively autocorrelated under the limits-to-arbitrage
hypothesis but have no significant autocorrelation under the volatility-
learning hypothesis. A second regression-based test to distinguish the two
hypotheses looks specifically at the demand for call and put options that are
close to at-the-money (ATM). These options have the greatest demand from
informed volatility traders because they have the highest volatility
sensitivity. Under the volatility-learning hypothesis, where the market maker
learns most from ATM options demand, the rest of the smile should move in
tandem with ATM implied volatilities. For instance, if volatility is
anticipated to rise (fall) then volatility-informed traders would buy (sell)
straddles, so the demand for calls should behave similarly to the demand for
puts. This way, the entire smile should move along with ATM volatility. By
contrast, under the limits-to-arbitrage hypothesis the implied volatility in
each moneyness category need not be related to changes in ATM volatility.

Following Kang and Park, (2008) a later strand of the literature hypothesizes
the co-existence of two different types of informed traders. In addition to
the volatility-motivated type, who has advanced information about volatility,
the directional-motivated type possess privileged information about the
direction of future movements in the price of the underlying asset. Therefore,
if we assume that traders in options markets have the most sophisticated
access to privileged information, any finding of volatility and/or directional
motivated buying pressure could be used by market makers to infer likely
movements in future (such as a rise in price or a reduction in volatility) as
a signal to rebalance their portfolios. The two distinct types of informed
traders have strong incentives to trade options, but with different order
imbalances, and therefore also different types of buying pressure on the
market maker, and consequently different impacts on implied volatility
changes. Again, and by contrast with the limits-to-arbitrage hypothesis, both
these hypotheses predict no autocorrelation in the dynamics of implied
volatility surfaces.

Kang and Park, (2008) and Chen and Wang, (2017) extend the regression
specification to include other buying pressure metrics and examine how ATM
options demand affects the demand for options in other moneyness categories.
When the informed traders are volatility-motivated, but have no knowledge
about the direction of price changes, volatility shocks would shift the
options supply curves and consequently also affect the smile. In this case,
and as already argued above, it is the demand for ATM options that should
mainly drive the entire smile and the implied volatilities of other options
should move alongside. By contrast, when the informed traders are directional-
motivated but have no knowledge about the size of future price changes, this
generates different buying pressures on calls relative to puts. For instance,
if the price is thought to rise, directional-informed traders would buy calls
and sell puts so the net buying pressure would be positive on calls and
negative on puts.

The extant empirical literature only examines established options markets.
Some papers confirm the limits-to-arbitrage hypothesis and find no evidence to
support either learning hypothesis. These include: Bollen and Whaley, (2004)
for S&P 500 index and stock options; Chan et al., (2004) for Hang Seng index
options; Shiu et al., (2010) for TAIEX index options and Chuang et al., (2020)
for VIX options. Kang and Park, (2008) test the directional-learning
hypothesis against limits-to-arbitrage and conclude that KOSPI 200 index
options implied volatilities are largely driven by directional trading.
Further extending the net buying pressure metrics to distinguish between
volatility-informed and directional-informed learning hypotheses, Chen and
Wang, (2017) conclude that both directional and volatility motivated demand
drive implied volatility changes in the TAIEX options market. This result is
supported for the KOSPI 200 market by Ryu et al., (2021)

We contribute to this literature in several respects. First, previous studies
focus on established and regulated options markets, where sophisticated
traders generally lead the market (Lakonishok et al.,, 2007). We examine
bitcoin options, which are traded in many different venues, most of them being
self-regulated, and consequently there are concerns about market mature and
price and volume manipulation – see Makarov and Schoar, (2020), Griffin and
Shams, (2020), Cong et al., (2020) and others. In 2019, the US Securities and
Exchange Commission (SEC) were persistently refusing applications to list
bitcoin exchange-traded funds, their reason being that the market is not
sufficiently mature.333See the Coindesk report: What to Make of the SEC’s
Latest Bitcoin ETF Rejection. Our results could somehow alleviate regulator
concerns about market immature by showing Deribit bitcoin options have been
aggregating volatility and directional information more efficiently since
2019. However, it does not help to alleviate concerns over manipulation. In
fact, while spot bitcoin ETF applications are still not succeeding, the reason
given nowadays is the presence of informed traders using private information
to manipulate bitcoin prices.444See the Bloomberg report: SEC Rejects VanEck’s
Bitcoin ETF in Latest Spot-Listing Snub.

Secondly, the highly volatile nature of bitcoin leads to compelling demand for
options to manage both volatility and direction risk (Alexander et al.,, 2020;
Alexander et al., 2021a, ; Deng et al.,, 2020; Scaillet et al.,, 2020). To
meet these demands Deribit (and other bitcoin options platforms) offers
extremely short-term 1-day and 2-day options, as well as one-, two- and three-
weekly listings, plus the more standard quarterly expires. The very short-term
maturities (1-day and 2-day) are unique to crypto options, and on the Deribit
bitcoin platform they constitute almost 20% of the total volume. Therefore, we
are able to disaggregate net buying pressure metrics and the subsequent
regression results into different maturity buckets to investigate the type of
informed trader operating at all points along the term structure of options
maturities.

Thirdly, whereas margin requirements on established stock and index options
exchanges are directly linked to the underlying volatility, Deribit and many
other self-regulated bitcoin options platforms offer up 100X leverage. These
markets also trade 24 hours a day, every day of the year. This way they
attract a broad participation from many uninformed speculators, not only from
informed professional traders and arbitragers. All these features are unique
to bitcoin option markets, and they could generate option trading motivations
and consequent bitcoin price movements that are very different from those
previously documented in established options markets.

Among other results, we find that both volatility and directional-motivated
demands drive short and medium term OTM and DOTM options prices, whereas only
directional trading drives prices of longer-term OTM calls and only volatility
information drives prices of longer-term DOTM puts. How could bitcoin option
traders benefit from understanding these driving force behind options of
different moneyness? Suppose a trader believes that the bitcoin market is
about to enter a particularly volatile month ahead – perhaps as a result of
heightened economic uncertainty, or because sentiment indicators based on
twitter, reddit or other social media sites are sending mixed signals. Then
the trader should enter a bearish risk reversal strategy by writing DOTM calls
and using the premium to buy DOTM puts of the same maturity. The strategy
would make a profit in the event that the trader’s beliefs about volatility
are borne out within the life of the options.

Our empirical results clearly confirm the limits-to-arbitrage hypothesis. On
the two learning hypotheses, we find strong evidence of trades based on
volatility information regardless of option moneyness categories, but the
directional-learning effect is less pronounced in ATM options. Directional-
motivated demand is mainly significant in out-of-the money (OTM) and deep-out-
of-the money (DOTM) options. We propose the following economic reasons why
there is more informed trading on privileged volatility information than on
information about directional price changes: (i) the fundamental value of
bitcoin and its return drivers (Zhang et al., (2021)) are far from clear and
not widely acknowledged, so it is not easy to be informed by directional
changes;555As shown in the literature, bitcoin price could be driven by market
sentiment and economic policy uncertainty (EPU), see twitter of Shen et al.,
(2019) and the economic policy uncertainty (EPU) of Demir et al., (2018). (ii)
bitcoin spot and derivatives markets are highly segmented so price discovery
can shift rapidly from one derivatives market to another; and (iii) bitcoin is
very much more volatile than equities, so ATM options have unusually high
volatility sensitivity, especially at longer maturities.

The unregulated less mature bitcoin options market differs from the well-
developed S&P 500 index options market in several aspects: (i) bitcoin options
market trade much more short term options (less than 7-day) that have much
greater market risk and are more sensitive to volatility than longer term
options. Additionally, bitcoin options call-put ratios is about 54:46 but
about 4:6 for the S&P 500 options. Those implies bitcoin option traders are
less risk averse than S&P 500 option traders; (ii) bitcoin options have a much
more symmetric smile. The slopes of S&P 500 implied volatility curves become
more negative with increasing fears of a stock market crash, while the
negative left slope and positive right slope of bitcoin options smiles
indicate that both positive and negative price jumps are expected; and (iii)
bitcoin volatility risk premium is consistently negative, much larger in
magnitude than that of S&P 500 options. This shows bitcoin option market
makers find it more difficult to hedge their inventory risk – due to the price
jump risk and less liquidity – and hence charge a higher risk-premium.

To investigate net buying pressure at different maturities, we apply the
methodology of Chen and Wang, (2017) to three different subsets of options
according to their maturities. Given the volume of trading on extremely short-
term options, we use ‘short-term’, ‘medium-term’, and ‘longer-term’ to group
options with maturities lying in the categories $[1,7]$, $[8,21]$ and $\geq
22$ days. We select these buckets so that trading volume is approximately
equal in each. Even though the volatility sensitivity increases with maturity,
we find that volatility-informed traders prefer short- and medium-terms
options. Nevertheless, volatility information does drive the prices of longer-
term, DOTM puts. But it is directional trading that dominates prices of
longer-term OTM calls. Overall, longer-term options encompass less informed
trades than short- and medium-term options.

Because we use hourly data we can also examine time-of-day patterns in the
buying pressures on bitcoin options. A recently emerging hour-of-day pattern
shows that the strongest directional demand pressure comes during Asian
trading times, whereas volatility-motivated demand is strongest while European
markets are open. Quite interesting, although European trading time has
largest volatility-demand, it has less information. ATM options are mainly
driving by volatility-motivated demand during Asian and US trading time. This
finding is in line with the volatility-transmission results of Alexander et
al., 2021b  who show that most volatility transmission occurs during US and
Asian trading times. Also directional learning is only supported in OTM and
DOTM option categories during Asian and US trading time slots.

The trading volumes on bitcoin options were very low during 2017 and 2018 so
we do not report our results on these years here but they are available on
request. By further disaggregating results year by year, we find that
volatility- and directional-informed traders only emerged after 2019. The
scale of informed trading has continually increased since then, and we
conclude that the Deribit market place is now rapidly evolving into a venue
for the efficient aggregation and dissemination of both directional and
volatility information.

The remainder of this paper is organized as follows: Section 2 describes the
Deribit options market and compares its implied volality curve to S&P 500
index options market; Section 3 uses hourly data aggregated from tick-level
transactions to report different measures of net buying pressure; Section 4
summarises the regression models and relates parameter estimates to tests for
the different hypotheses; Section 5 presents our empirical results for options
of different moneyness, maturities and time-of-day; and Section 6 concludes
the paper.

##  2  A Comparison of Bitcoin and S&P 500 Options Markets

The online trading platform Deribit was launched in the Netherlands in June
2016 but during 2021 it moved registration to the Republic of Panama, thus
escaping the scrutiny of European derivatives regulators. The listed products
are perpetuals, fixed-expiration futures and options on only two USD rates,
versus bitcoin and ethereum respectively. At the time of writing, Deribit
currently accounts for about 80% of bitcoin option trading volume across
global exchanges, most of the other 20% being traded on other self-regulated
centralised exchanges such as OKEx, LedgerX and Huobi.666See reports: skew and
Deribit is Dominating Bitcoin Options With 78% Market Share: Here’s How They
Did It. Due to the extreme volatility of bitcoin prices, both directional and
volatility motivated demand could be present in these options.

S&P 500 European index options are margined and cash-settled in USD. The well-
developed and regulated Chicago Board Options Exchange opens at 8:30 a.m.
central time and closes at 3:15 p.m. central time from Monday to Friday each
week. Global trading after hours is also available from 7:15 p.m. to 8:15 a.m.
Monday to Friday. The bitcoin options listed on Deribit are also European
style, but they trade continuously every day of the year – the market never
closes. They are margined and cash-settled in bitcoin instead of a fiat
currency such as USD. The underlying is the Deribit bitcoin index price (BTC)
that is an equally weighted average of bitcoin USD spot prices on several
leading spot exchanges such as Bitstamp, Gemini, Bitfinex, Bittrex, Itbit,
Coinbase, LMAX Digital and Kraken. Exchanges having invalid data or delayed
order book are excluded in calculating the index price. The nominal value of
each option is 1 BTC and settlement is at 8:00 UTC time (coordinated universal
time). The exchange lists a rich variety of standard European calls and puts
with expiry dates ranging from 1-day to a maximum of 12 months. Starting in
2019, the demand from traders to hedge and speculate over a very short horizon
led to the continual issuance of 1-day and 2-day options as well as 1-week,
2-week and (more recently) 3-week options.

Table 1 decomposes the total volume traded on all bitcoin options per year,
using our own categorisation of these options into short-term (1 – 7 days),
medium-term (8 – 21 days) and longer-term options ($\geq$ 22 days). As more
new expires of short- and medium-term bitcoin options are introduced the most
liquid bitcoin options have less than seven days to maturity, trading volume
increasing from 19.17% in 2018 to 38.09% in 2021. As for S&P 500 index
options, the share of weekly options (1 – 7 days) increases from 21.86% in
2017 to 28.01% in 2020 and medium-term options (8 – 90 days) accounts for over
50% of total volume. In most markets the prices of short-term option prices
are more volatile than prices of long term options, due to the gamma effect.
Unlike S&P 500 options traders, bitcoin options traders focus mostly on short-
term options, which supports the view that bitcoin options traders are less
risk averse than S&P 500 options traders. Also, the net-buying-pressure
literature on S&P 500 usually focuses on medium term options, because of this
volume imbalance. By contrast, the much larger volume share of short-term
options, which seems unique to bitcoin options market, motivates us to include
them in our empirical study. If the bitcoin market becomes less volatile over
time, and attracts more institutional investors, we might expect a trading
volume distribution closer to that of S&P 500 index options.

Table 1: Deribit and S&P 500 Option Trading Volume: Percentages by Maturities

Time to Maturity | 2017 | 2018 | 2019 | 2020 | 2021
---|---|---|---|---|---
| Deribit Bitcoin Option
1-7 days | 27.35% | 19.17% | 35.31% | 42.19% | 38.09%
8-21 days | 21.46% | 14.41% | 26.73% | 27.18% | 30.54%
$\geq$ 22 days | 51.18% | 66.42% | 37.96% | 30.63% | 31.38%
| S&P 500 Index Option
1-7 days | 21.86% | 21.21% | 23.43% | 28.01% |
8-90 days | 66.95% | 67.43% | 61.30% | 54.33% |
$\geq$ 91 days | 11.19% | 11.37% | 15.27% | 17.66% |

Note. The figures above are from millions of tick-by-tick Deribit bitcoin
options trades from 1 January 2017 to 28 July 2021 accessed via the Deribit
application program interface, which no longer provides historical data but
our sample can be accessed from Tardis or CoinAPI. The sample stops after July
2021 because there are data only for very short maturity trades. Daily
frequency S&P 500 index options data is from Wharton Research Data Services.
It has 8,688,408 entries, containing 4,362,860 (50.21%) calls and 4,325,548
(49.79%) puts, but the data is only available until 2020.

In addition to option expiration date, strike (in USD) and type (European call
or put), our bitcoin option tick-by-tick data includes details about the
trading direction (i.e. whether buyer or seller initiated), the implied
volatility, the option price (in BTC), the traded amount (in BTC), the
underlying bitcoin index price (in USD) and the timestamp in milliseconds. The
full data-set contains 3,431,071 entries consisting of 1,834,499 (53.47%) call
options and 1,594,420 (46.47%) put options. For 2,152 (0.062%) of trades the
option type was missing. The Deribit exchange imposes an upper bound of 500%
and a lower bound of 0% for their implied volatility quotes due to concerns of
data outliers and illiquidity. This way another 2,447 (0.71%) of the full
data-set were excluded. The cleaned final data-set contains 3,427,160 entries
consisting of 1,833,838 (53.51%) calls, and 1,593,322 (46.49%) puts.

Options of different strikes $K$ and maturities $T$ are classified by their
Black-Scholes deltas777Other authors use $K/S,\ \log(K/S)$ and $K/Se^{-rT}$ to
measure moneyness. We also tried these alternatives, but found virtually no
difference in our qualitative conclusions. The S&P 500 options data already
contains Black-Scholes $\Delta$ and since this metric is also standard in the
net buying pressure literature, we also use $\Delta$., viz.

$\displaystyle\Delta^{C}_{t}(F_{t},\sigma|K,T)$
$\displaystyle=\Phi\left[\frac{\ln\left(F_{t}/K\right)+0.5\sigma^{2}\tau}{\sigma\sqrt{\tau}}\right]\quad\mbox{and}\quad\Delta^{P}_{t}(F_{t},\sigma|K,T)=\Delta^{C}_{t}(F_{t},\sigma|K,T)-1,$
(1)

where $\Phi[\cdot]$ is the standard cumulative normal distribution function,
$S_{t}$ is the underlying price (USD), $F_{t}=S_{t}e^{r\tau}$ is the forward
price (USD), $K$ is the strike price (USD), $\sigma$ is the annualised
volatility, $\tau=T-t$ is the residual time to maturity in years and we use
$C$ for a call and $P$ for a put.888We only use the Black-Scholes model to
recover implied volatilities and deltas in order to group options into
different moneyness categories. Of course, a geometric Brownian motion is not
suitable to model the bitcoin underlying price – stochastic volatility models
such as those in Tiwari et al., (2019) or Siu and Elliott, (2021) would be
preferable. Following Bollen and Whaley, (2004), most papers in the literature
set $\sigma$ equal to the realised volatility, calculated as the annualised
square root of the average sum of squared log returns over the most recent
$n$-days.999The choice for $n$ differs according to the data frequency. For
instance, Bollen and Whaley, (2004) use 60 days for their daily data, and Kang
and Park, (2008) and Chen and Wang, (2017) both use 60 days for their 5-minute
data. We use a 15-day realised volatility based on bitcoin daily log returns,
the same $\sigma$ for all options. Of course, using the option’s own implied
volatility for dynamic delta hedging but using a physical measure of
volatility for calculating the option’s moneyness is a standard practice in
this literature – it is attractive because it avoids any endogeneity concerns
in our regressions where the dependent variable is implied volatility.
Besides, it is important to note that (i) we only use this to classify options
into five moneyness categories, and (ii) our results are robust to alternative
choices for $\sigma$.101010Using a 15-day realised volatility is, of course,
ad hoc. So we explored some alternatives for $\sigma$ which slightly change
the way that options are assigned to moneyness categories. We analysed results
for a 30-day realised volatility, using the option’s own implied volatility,
and using a simpler definition of moneyness as the ratio of the underlying
price to the strike of the option, as in Ryu et al., (2021). We found
virtually no difference in the qualitative conclusions to be drawn from our
analysis. Detailed results are available from the authors on request.  Now we
use the option deltas to allocate them into one of five moneyness categories,
as follows:111111Options with absolute delta below 0.02 or above 0.98 are
excluded because of the distortions due to stale prices and illiquidity.

  * •

Deep-out-of-the-money (DOTM): $0.02<|\Delta|\leq 0.125$,

  * •

Out-of-the-money (OTM): $0.125<|\Delta|\leq 0.375$,

  * •

At-the-money (ATM): $0.375<|\Delta|\leq 0.625$,

  * •

In-the-money (ITM): $0.625<|\Delta|\leq 0.875$,

  * •

Deep-in-the-money (DITM): $0.875<|\Delta|\leq 0.98$.

Table 2: Trading Volume Across Five Moneyness Categories

| 2017 | 2018 | 2019 | 2020 | 2021
---|---|---|---|---|---
| Call | Put | Call | Put | Call | Put | Call | Put | Call | Put
| Deribit Bitcoin Option
DOTM $(\%)$ | 2.86 | 10.34 | 18.44 | 7.75 | 14.62 | 13.83 | 12.74 | 12.78 | 13.71 | 13.43
OTM $(\%)$ | 13.93 | 16.85 | 21.66 | 13.24 | 21.12 | 20.15 | 21.74 | 21.41 | 22.61 | 23.01
ATM $(\%)$ | 26.27 | 9.10 | 16.24 | 7.73 | 12.86 | 9.11 | 14.39 | 11.04 | 12.87 | 9.74
ITM $(\%)$ | 14.47 | 2.13 | 7.20 | 4.05 | 4.46 | 2.17 | 3.38 | 1.28 | 2.54 | 1.12
DITM $(\%)$ | 3.53 | 0.53 | 1.61 | 2.08 | 1.16 | 0.52 | 1.04 | 0.20 | 0.71 | 0.25
Total Prop. $(\%)$ | 61.06 | 38.94 | 65.15 | 34.85 | 54.22 | 45.78 | 53.29 | 46.71 | 52.44 | 47.56
# T.C. (Million) | 0.02 | 0.02 | 0.21 | 0.09 | 0.70 | 0.60 | 2.36 | 2.08 | 1.38 | 1.32
T.V. ($\$$Billion) | 0.16 | 0.10 | 0.93 | 0.50 | 4.27 | 3.60 | 23.59 | 20.68 | 53.99 | 48.97
| S&P 500 Index Option
DOTM $(\%)$ | 9.28 | 25.65 | 10.91 | 21.57 | 9.04 | 23.89 | 9.04 | 21.58 |  |
OTM $(\%)$ | 13.99 | 22.20 | 15.38 | 22.21 | 14.18 | 21.27 | 13.45 | 22.97 |  |
ATM $(\%)$ | 12.93 | 11.00 | 11.70 | 12.62 | 14.27 | 12.76 | 13.51 | 13.44 |  |
ITM $(\%)$ | 2.80 | 1.21 | 2.25 | 2.35 | 2.55 | 1.29 | 2.86 | 2.00 |  |
DITM $(\%)$ | 0.79 | 0.15 | 0.48 | 0.53 | 0.48 | 0.27 | 0.67 | 0.47 |  |
Total Prop. $(\%)$ | 39.79 | 60.21 | 40.72 | 59.28 | 40.52 | 59.48 | 39.54 | 60.46 |  |
# T.C. (Million) | 88.37 | 133.70 | 113.60 | 165.40 | 88.45 | 129.81 | 82.30 | 125.86 |  |
T.V. ($\$$Billion) | 168.95 | 179.76 | 311.98 | 439.71 | 289.06 | 331.36 | 537.93 | 751.90 |  |

  * •

Note. The total number of traded contracts (T.C.) and USD trading volume
(T.V.) by year and the proportion traded in each moneyness category, are
decomposed into calls and puts. The notional value per bitcoin option contract
is 1 bitcoin and one point of S&P 500 index option is 100 USD.

Table 2 reports the total number of traded contracts and USD trading volumes
on all options by year (in USD billion, last line) and decomposes this into
proportions traded in each moneyness category above, and into calls and puts
within each category. The annual number of traded contracts of S&P 500 options
is quite stable, siting at roughly 200 million per year, except 279 million in
2018. The bitcoin options total USD trading volume increases 400-fold, from
only 0.26 USD billion in 2017 to 102.96 USD billion in 2021 and the total
number of traded contracts increases 111-fold from 0.04 million in 2017 to 4.4
million in 2020. Another difference is that the S&P 500 call-put ratio is
almost identical, around 4:6 from 2017 to 2020, while traders prefer bitcoin
calls instead of puts and the bitcoin call-put ratio changed significantly,
from about 65:35 in 2018 to about 54:46 after 2019. This shows that the
bitcoin options market has less risk-averse investors than the S&P 500 options
market, which is led by sophisticated institutional traders who demand out-of-
the-money puts to hedge downside and crash risk, see Kelly et al., (2016).

The two options markets demonstrate a similar volume distribution for
different moneyness categories, where OTM, DOTM and ATM options are the most
traded contracts and trades on ITM and DITM options are seldom – less than 4%
for both bitcoin and S&P 500 options. This is to be expected, because the call
(put) option price increases rapidly as the strike decreases (increases). For
instance, in the bitcoin options market during 2021 (January to July) total
volume reached 52.44 USD billion for calls and 47.56 USD billion for puts, and
3.25% of the total volume was traded on ITM and DITM calls and even less,
1.37%, on puts. The left and right panels of Figure 1 depict how the
percentages of total trading volume in the five moneyness categories have
changed over time for S&P 500 and bitcoin options respectively. The pattern of
S&P 500 options is quite stable where OTM, DOTM and ATM are the most traded
contracts with shares about 32%, 35% and 25% respectively. Although much
variability shown in 2017 and 2018, where OTM bitcoin options increase from
30% in 2017 to over 45% in 2021, the shares of bitcoin options are converging
together during 2019-2021 to similar pattern (even in magnitude) as for S&P
500 options. This indicates the bitcoin options market only really started
maturing in 2019, so more recent data are likely to be more reliable and not
distorted by stale prices or low trading volumes.

Figure 1: S&P 500 and Bitcoin Options Volume Percentage by Moneyness
Categories

Note. The left and right panels plot the trading volume percentages by
moneyness categories of S&P 500 and bitcoin options accordingly. The pattern
of S&P 500 options is quite stable where OTM, DOTM and ATM are the most traded
contracts with shares about 32%, 35% and 25% respectively. After 2019, the
shares of bitcoin options are converging to a pattern (even in magnitude) very
similar to that of the S&P 500 options.

Now we compare and contrast the implied volatility curves of bitcoin and S&P
500 options, interpreting the implications of their similarities and
differences for bitcoin option traders. As shown in Table 3, bitcoin realised
volatility (RV) and implied volatility (IV) are both much larger (around
4-times in 2018 and 2019) than the corresponding metrics for S&P 500 options –
although, in line with our observation from Tables 3 and 4, a trend of
decreasing volatility in bitcoin is perceived as the options market matures.
The volatility risk premium, as measured by the realised-implied volatility
spread (VS = RV-IV) is consistently negative and much larger in magnitude for
bitcoin options. This is not surprising because bitcoin has a great risk of
price jumps and some options have low liquidity, making it more difficult for
bitcoin options market makers to hedge their inventory risk. In compensation,
for holding this risk they can charge a higher volatility risk premium than
S&P 500 options market makers.

Table 3: Realised Volatility, Implied Volatility and Volatility Spread

| Bitcoin Option | S&P 500 Index Option |
---|---|---|---
Year | RV | IV | VS | RV | IV | VS | IV Correlation
2017 | 0.93 | 1.05 | -0.12 | 0.08 | 0.17 | -0.09 | 0.02
2018 | 0.85 | 0.97 | -0.12 | 0.17 | 0.20 | -0.03 | -0.02
2019 | 0.65 | 0.80 | -0.15 | 0.15 | 0.19 | -0.04 | 0.07
2020 | 0.64 | 0.76 | -0.12 | 0.32 | 0.31 | 0.002 | 0.17

Note. The implied volatility (IV) is calculated as the average of all trades
in each year and the realised volatility is calculated as the annualised
square root of the average sum of squared log returns over the most recent
15-days. The realised-implied volatility spread (VS=RV-IV) measures the risk-
premium charged by market markers for providing liquidity and compensating
inventory risk.

Table 4: Implied Volatility Curve

| Deribit Bitcoin Option | S&P 500 Index Option
---|---|---
Year | Level | Left Slope | Right Slope | Level | Left Slope | Right Slope
2017 | 0.996 | -0.035 | 0.045 | 0.108 | -0.312 | -0.200
2018 | 0.868 | -0.026 | 0.050 | 0.142 | -0.296 | -0.166
2019 | 0.716 | -0.032 | 0.023 | 0.142 | -0.285 | -0.180
2020 | 0.618 | -0.081 | 0.039 | 0.247 | -0.284 | -0.176
mean | 0.799 | -0.044 | 0.039 | 0.160 | -0.294 | -0.180

Note. The level is calculated as the average of all ATM calls and puts in each
year, regardless of expiration. The left slope is defined as the ratio of
difference between IVs of category 2 and category 3 options to the IV level,
while the right slope is the ratio of difference between IVs of category 3 and
category 4 options to the IV level. Category 2: ITM calls and OTM puts.
Category 3: ATM calls and ATM puts. Category 4: OTM calls and ITM puts.

Figure 2: Relative-to-ATM Implied Volatility Smile and Slopes

Note. To make the much higher bitcoin IVs comparable to S&P 500 options, we
scale implied volatilities of all categories by its own ATM IV. Top panel: it
plots implied volatilities relative to ATM options’ IV for the five
categories. Bottom panel: it shows the weekly average of left and right slopes
from 2017 to 2020. The left slope is defined as the ratio of difference
between IVs of categories 2 and 3 options to ATM IV, while the right slope is
the ratio of difference between IVs of categories 3 and 4 options to ATM IV.

To characterise the implied volatility curve (IVC), we group implied
volatilities (IV) as follows: Category 1: DITM calls and DOTM puts. Category
2: ITM calls and OTM puts. Category 3: ATM calls and ATM puts. Category 4: OTM
calls and ITM puts. Category 5: DOTM calls and DITM puts. Then, to make the
much larger bitcoin and S&P 500 options IVs on a comparable scale, we divide
implied volatility for all categories by the implied volatility of ATM options
in Category 3. Additionally, following the literature, we use the terminology
IV level to denote the average IVs of ATM calls and puts, left slope is the
difference between average IVs of Category 2 and Category 3 options, divided
by the IV level, and right slope is the difference between average IVs of
Category 3 and Category 4 options, divided by the IV level. Table 4 reports
the results and Figure 2 depicts them. They demonstrate several importance
differences between bitcoin and S&P 500 options IVs.

First, from Table 3, the bitcoin IV level is roughly five times larger than
that of S&P 500 options, and only in bitcoin there is a downward trend in
average IV level – it decreases year by year as the bitcoin spot and options
markets mature over time. Second, as seen in both the Table 4 and Figure 2 the
S&P 500 options IVC is much steeper than that of bitcoin options and its
typical ‘skew’ shape is not mirrored by bitcoin options, which have a much
more symmetric smile. This is not surprising given their statistical
properties: the S&P 500 realised skewness (-0.732) is negative and about ten
times the size of the bitcoin realised skewness (-0.0715), and the realised
kurtosis is greater in bitcoin. Bakshi et al., (2003) show that the IVC is
shaped by the skewness and kurtosis in the physical measure: the more negative
the skewness, the steeper the implied volatility curve. The left and right
slopes of S&P 500 options are both negative, downward-sloping and rather
stable across time, around -0.3 and -0.2 accordingly. In contrast, the left
slope of bitcoin implied volatility curve is negative with four years average
-0.044 and the right slope is positive with four years average 0.039. The
bottom panel of Figure 2 plots the evolution of the left and right slope
measures over time. The slopes of S&P 500 implied volatility curves become
more negative with increasing fears of a stock market crash, while the
negative left slope and positive right slope of bitcoin smiles indicate that
both positive and negative price jumps are expected.

Clearly, bitcoin and the S&P 500 index are driven by different underlying
jump-diffusion stochastic processes. For instance, Yan, (2011) proves that the
implied volatility slope is approximately proportional to the average jump
size and jump intensity of the underlying price process, and Scaillet et al.,
(2020) found a total 124 large jumps in the bitcoin price, containing 70
positive and 54 negatives jumps, during the period 26 June 2011 to 29 November
2013 alone.

##  3 The Information Content of Bitcoin Options

We begin this section by examining the relationship between the change in
bitcoin option trading volume $\Delta v$ or the aggregated net-buying-pressure
(i.e. the order imbalance) and one-period-ahead bitcoin spot return or
volatility, either realised and implied. We perform three separate sets of
regressions that test the predictive power of volume and order-imbalance
information metrics for bitcoin spot and/or options prices. First, to measure
order imbalance over a time period between time $t-1$ and time $t$, we define
the order imbalance $N_{t}$ as the difference between the aggregated volumes
on all buyer-initiated trades and seller-initiated trades, each multiplied by
the absolute value of the options delta, i.e.:

$\displaystyle
N_{t}=\sum_{i=1}^{m_{t}}{B_{i,t}\times\left|\Delta_{i,t}\right|}-\sum_{i=1}^{n_{t}}{S_{i,t}\times}\left|\Delta_{i,t}\right|,$
(2)

where $B_{i,t}$ is the volume on the $i^{th}$ buyer-initiated trade during the
interval between time $t-1$ and time $t$, and $S_{i,t}$ is the equivalent
quantity for seller-initiated trading volume, and $|\Delta_{i,t}|$ is the
absolute value of the delta of the option that is traded. This way, the buying
side is aggregated over $m_{t}$, the number of of buyer-initiated trades
between times $t-1$ and $t$, and the selling side is summed over $n_{t}$, the
corresponding number for seller-initiated trades. Using these data we run the
following regressions:

$\displaystyle{x_{t}=\gamma_{0}+\gamma_{1}\cdot x_{t-1}+\gamma_{2}\cdot
y_{t-1},\qquad x\in\\{r,\Delta IV,\Delta RV\\},\quad y\in\\{\Delta v,N\\}}.$
(3)

Table 5: Information Content of Option Trading

|  | Volume, $\Delta v$ | Aggregate Order Imbalance, $N$
---|---|---|---
|  | $\gamma_{0}$ | $\gamma_{1}$ | $\gamma_{2}$ | $\gamma_{0}$ | $\gamma_{1}$ | $\gamma_{2}$
| 1-Hour | $0.0001^{***}$ | $-0.053^{***}$ | $0.27^{***}$ | $0.0001^{***}$ | $-0.053^{***}$ |  $8.43$e-7
Return | 1-Day | $0.002^{***}$ | $-0.084^{***}$ | $0.51^{***}$ | $0.0016^{***}$ | $-0.086^{***}$ |  $-1.38$e-6
| 5-Days | $0.016^{***}$ | $-0.025$ | $0.068$ | $0.018^{***}$ | $-0.0027$ |  $-6.08$e-6
| 1-Hour | $-0.0019^{***}$ | $-0.42^{***}$ | $4.27^{***}$ | $-0.0021^{***}$ | $-0.42^{***}$ |  $6.36$e-5∗∗∗
IV | 1-Day | $-0.0036^{***}$ | $-0.067^{***}$ | $3.32^{***}$ | $-0.0055^{***}$ | $-0.11^{***}$ |  $3.96$e-5∗∗∗
| 5-Days | $-0.0077$ | $0.14^{***}$ | $1.73^{***}$ | $-0.010^{***}$ | $0.057$ |  $3.02$e-6
| 1-Hour |  $-1.02$e-5∗∗∗ | $0.034^{***}$ | $0.18^{***}$ |  $-1.49$e-5∗∗∗ | $0.031^{***}$ |  $4.35$e-7∗∗∗
RV | 1-Day | $-0.0007^{***}$ | $0.41^{***}$ | $0.30^{***}$ | $-0.0012^{***}$ | $0.39^{***}$ |  $9.94$e-6∗∗∗
| 5-Days | $-0.0078$ | $0.35^{***}$ | $-0.48$ | $-0.014^{***}$ | $0.35^{***}$ |  $2.89$e-5∗∗∗

  * •

Note. This table reports the regression result
$x_{t}=\gamma_{0}+\gamma_{1}\cdot x_{t-1}+\gamma_{2}\cdot y_{t-1}$. Here
$x_{t}$ is the bitcoin price return or $\Delta IV$ or $\Delta RV$; and $y_{t}$
is the change of bitcoin options trading volume $\Delta v_{t}$ or the order
imbalance measured by $N_{t}$. The ∗∗∗ indicates 1% significance level.

The results are displayed in Table 5. Several highly significant estimates for
$\gamma_{2}$ confirm that hourly trading volume has a significant positive
effect on returns and realised volatility over the next hour, and a similar
positive causation is clear from our regressions of daily returns or realised
volatility on the previous day’s trading volume. Options trading volume has an
even greater effect on future implied volatility, where the significance in
implied volatility (and therefore also option prices) persists even for the
next five days. Hourly and daily net buying pressure also have a highly
significant effect on both realised and implied volatilities.

In contrast to trading volume, order imbalance during the hourly, daily or
5-day interval has no predictive power for returns over the next interval.
This is understandable, and supported by our empirical analysis later in this
paper, where we show that order imbalance is motivated more by volatility
information than information about the direction of the underlying price, i.e
about the sign and size of the return. And in supporting of later results,
order imbalance does have predictive power for implied and realised
volatilities. So overall, the results in Table 5 suggest that bitcoin options
traders may indeed possess superior, if short-lived, information about the
future direction of bitcoin spot and option prices that would allow them to
generate abnormal returns by developing a suitable trading strategy for
bitcoin options.

Section 2 has demonstrated that the bitcoin options market is less mature than
the S&P 500 options market. Spot prices have more frequent positive as well as
negative jumps, and bitcoin option traders appear less risk averse than S&P
500 options traders. Hence, we might expect different trading motives to drive
the bitcoin options implied volatility curve compared with other well-
regulated, more mature markets such as the S&P 500 options market. To
investigate these motives we start by following Bollen and Whaley, (2004) to
define the net buying pressure at time $t$ in moneyness $k$, denoted
$A^{k}_{t}$ as the difference between buyer-initiated trades and seller-
initiated trades multiplied by the absolute value of the options Black-Scholes
delta. More precisely, we also divide net buying pressure to separate that on
calls from that on puts, therefore defining it as:

$\displaystyle
A_{j,t}^{k}=\sum_{i=1}^{m_{jk,t}}{B_{ij,t}^{k}\times\left|\Delta_{ij,t}^{k}\right|}-\sum_{i=1}^{n_{jk,t}}{S_{ij,t}^{k}\times}\left|\Delta_{ij,t}^{k}\right|,$
(4)

where $j\in\left\\{\mbox{Call, Put}\right\\}=\left\\{C,P\right\\}$,
$k\in\left\\{\mbox{DOTM, OTM, ATM, ITM, DITM}\right\\}$ and $B_{ij,t}^{k}$
(resp. $S_{ij,t}^{k}$) is the buyer-initiated (seller-initiated) trading
volume on the $i^{th}$ option of type $j$ in moneyness category $k$. This is
aggregated over all buyer- or seller-initiated trades between time $t-1$ and
time $t$, weighted by the absolute value of $\Delta_{ij,t}^{k}$, the delta of
the option traded. This way, the buying pressure is aggregated over
$m_{jk,t}$, the number of of buyer-initiated trades on an option for type $j$
in moneyness category $k$, between times $t-1$ and $t$, and the selling
pressure is summed over $n_{jk,t}$, the corresponding number for seller-
initiated trades.

The original metric for net buying pressure defined above mixes directional-
informed and volatility-informed trading. Therefore, following Chen and Wang,
(2017) (also recently used in Ryu et al., (2021)), at each moneyness level $k$
we separately measure the directional-motivated demand for calls and puts,
calculated as:

$D_{C,t}^{k}=\frac{A_{C,t}^{k}-A_{P,t}^{k}}{2},\quad\mbox{and}\quad
D_{P,t}^{k}=\frac{A_{P,t}^{k}-A_{C,t}^{k}}{2}.$ (5)

Note that $D_{P,t}^{k}=-D_{C,t}^{k}$ by definition. Equation (5) captures
directional trading volume in that an anticipated rise (fall) in the
underlying price would induce a positive (negative) net demand for calls and
negative (positive) net demand for puts. That is, when directional traders
dominate the volume in moneyness category $k$, then $D_{C,t}^{k}>0$ indicates
an anticipation of a rise in the underlying price, whereas $D_{C,t}^{k}<0$
means the price is anticipated to fall. Also following Chen and Wang, (2017)
the volatility-motivated demand (which is the same for calls and puts) is
defined as:

$V_{t}^{k}=\frac{A_{C,t}^{k}+A_{P,t}^{k}}{2}.$ (6)

Equation (6) captures anticipated increasing (decreasing) in implied
volatility by volatility-informed traders, which would induce positive
(negative) net buying pressure on both calls and puts. That is, when
volatility traders dominate the volume in moneyness category $k$,
$V_{t}^{k}>0$ when these traders expect implied volatility to increase and
$V_{t}^{k}<0$ if they expect implied volatility to decrease.121212We could
also scale the directional and volatility-motivated demands by the total
delta-weighted volume
${TV}^{k}_{t}={\sum_{j\in\\{call,put\\}}\sum_{i=1}^{m_{jk,t}}{B_{ij,t}^{k}\times\left|\Delta_{ij,t}^{k}\right|}+\sum_{i=1}^{n_{jk,t}}{S_{ij,t}^{k}\times}\left|\Delta_{ij,t}^{k}\right|}$
and define the relative net-buying-pressures as
$\overline{D}_{C,t}^{k}=\frac{D_{C,t}^{k}}{{TV}^{k}_{t}},\qquad\overline{D}_{P,t}^{k}=\frac{D_{P,t}^{k}}{{TV}^{k}_{t}},\qquad\overline{V}^{k}_{t}=\frac{V_{t}^{k}}{{TV}^{k}_{t}}.$
The empirical results are available on request, but not reported here because
they are qualitatively unchanged. We thank an anonymous referee for bring this
robustness check to our attention.

We obtain an hourly time series for net buying volume, net buying pressure,
and directional- and volatility-motivated demand. For net buying volume we
aggregate volumes on all buyer-initiated trades during the 1-hour interval,
and similarly for the seller-initiated trades, and then take the difference.
For the other measures, we aggregate them using formulae (4)-(6). The previous
literature uses different time intervals for aggregation: daily frequency in
Bollen and Whaley, (2004), five-minutes in Kang and Park, (2008) and Chen and
Wang, (2017) and 1-minute in Ryu et al., (2021).

For illustration, Figure 3 contains six time series plots of directional- and
volatility-motivated net buying pressure during the last three years of the
sample, i.e. 1 January 2019 to 28 July 2021. The left panel exhibits the first
part from 1 January 2019 to 30 April 2020 and – on a different scale – the
right panel exhibits the second part, from 1 May 2020 to 28 July 2021. The
upper plots depict the net buying and selling volumes during the day, and the
remaining plots depict the dynamics of $V_{t}^{k}$ and $D_{t}^{k}$ for $k=$
DOTM, OTM, ATM, ITM and DITM. We observe that the time series increase
dramatically and are much more volatile after 1 November 2020 when the bitcoin
price rise from 10,000 USD to more than 60,000 USD in the space of a few
months.

Figure 3: The Dynamics of Directional- and Volatility-Motivated Net Buying
Pressure

Note. Net buying/selling volume on Deribit bitcoin options (top) and
volatility-motivated (red) and directional-motivated (blue) net buying
pressure for options in different moneyness categories, measured in USD
million. We only display the series for calls, because the respective measure
for puts is either the same (volatility-motivated) or the opposite sign
(directional-motivated). The left panels are from May 2019 to April 2020; the
right panels are from May 2020 to July 2021. The hourly measures are averaged
over each day and the plots exhibit these daily averages.

Table 6 reports the average net buying volume, and different measures of net
buying pressure on calls and puts, where the hourly data are now averaged over
each year in the sample. All metrics increase dramatically over time. For
instance, the annual average ATM net buying pressures shot up from 455 USD in
2017 to 94,818 USD in 2020. Traders consistently sell DOTM and OTM options and
buy ATM, DITM and ITM options over the entire period, except for the small net
selling of ITM and DITM put options in 2021. As a result, the net buying
pressure on ITM and DITM options is exceptionally large. Even though fewer
such options are traded, as noted from Table 2 above, the buyer-initiated
trades far outweigh the seller-initiated trades, particularly on calls. On
average during 2020, the net buying pressure on ITM calls is 109.48 USD
million, which is about 2/3rds of the buying pressure on ATM calls, and the
average net buying pressure on DITM calls is almost the same as for ITM calls.
This is much larger than is seen in standard markets. For instance, traders on
S&P 500 index options mostly buy DOTM and OTM puts for protection and sell
DITM and ITM calls for premiums in Kang and Park, (2008). The unusual demand
for ITM and DITM calls might be induced by unusually large directional-
motivated demand, probably based on the prediction of future price bubbles.
Such bubbles have been frequent, even during bitcoin’s short history (Cheah
and Fry,, 2015) and predictions of further bubbles are commonly and
consistently reported in the media.

Table 6: Average Hourly Net Buying Volume and Pressure

| 2017 | 2018 | 2019 | 2020 | 2021
---|---|---|---|---|---
| Call | Put | Call | Put | Call | Put | Call | Put | Call | Put
| Panel A. Net Buying Volume
DOTM | 35 | -380 | -1,646 | -1,035 | -21,544 | -20,385 | -64,920 | -15,895 | -233,394 | -164,373
OTM | -356 | 42 | -3,370 | -691 | -6,814 | -1,310 | -8,856 | -31,318 | 169,622 | -141,027
ATM | 959 | -209 | 469 | 290 | 8,691 | 3,757 | 36,455 | -13,410 | 207,075 | 233,671
ITM | 891 | 86 | 307 | -282 | 4,495 | 2,516 | 17,006 | 13,934 | 26,321 | -11,499
DITM | 391 | 25 | 351 | 895 | 945 | 487 | 12,689 | 1,459 | 18,442 | -2,174
Totals | 1,919 | -437 | -3,890 | -823 | -14,228 | -14,937 | -7,627 | -45,231 | 188,067 | -85,401
| Panel B. Net Buying Pressure
DOTM | 6 | -21 | -150 | -61 | -1,340 | -1,256 | -3,777 | -781 | -18,221 | -14,559
OTM | -124 | 49 | -635 | -162 | -1,256 | -67 | -1,029 | -8,669 | 64,381 | -18,015
ATM | 455 | -84 | 234 | 123 | 4,270 | 2,016 | 19,432 | -3,575 | 94,818 | 108,546
ITM | 659 | 62 | 229 | -211 | 3,127 | 1,854 | 12,395 | 10,213 | 16,297 | -10,498
DITM | 364 | 22 | 316 | 837 | 875 | 453 | 11,745 | 1,361 | 17,614 | -2,430
Totals | 1,360 | 26 | -7 | 526 | 5,676 | 2,999 | 38,767 | -1,451 | 174,889 | 63,045
| Panel C. Direction Net Buying Pressure for Calls
DOTM | 14 | -44 | -42 | -1,498 | -1,831
OTM | -87 | -236 | -594 | 3,820 | 41,198
ATM | 270 | 55 | 1,127 | 11,504 | -6,864
ITM | 299 | 220 | 637 | 1,091 | 13,397
DITM | 171 | -261 | 211 | 5,192 | 10,022
Totals | 667 | -266 | 1,338 | 20,109 | 55,922
| Panel D. Volatility Net Buying Pressure
DOTM | -8 | -105 | -1,298 | -2,279 | -16,390
OTM | -38 | -398 | -662 | -4,849 | 23,183
ATM | 185 | 178 | 3,143 | 7,929 | 101,682
ITM | 360 | 9 | 2,490 | 11,304 | 2,900
DITM | 193 | 576 | 664 | 6,553 | 7,592
Totals | 693 | 260 | 4,337 | 18,658 | 118,967

  * •

Note. Average net buying volume and net buying pressure in USD. Panels A and B
represent the average of hourly frequency net buying volume and net buying
pressure over an entire year.

Gemmill, (1996), Kelly et al., (2016) and others demonstrate that the S&P 500
options market is dominated by large, sophisticated institutional traders that
demand puts to hedge downside and crash risk. In line with this observation,
Bollen and Whaley, (2004) find that changes in implied volatility of S&P 500
options are most strongly affected by buying pressure for put options.
However, the interest of institutional traders in bitcoin options market is
still at a very early stage. There are relatively more speculative traders,
and these have risk-aversion characteristics that may be quite different from
the institutional traders in S&P 500 options. That is our main reason for
finding support for volatility-motivated demand where none is present in S&P
500 options. Furthermore, Derman, (1999) shows that the S&P index has range-
bounded, stable-trending and crash regimes. By contrast, bitcoin prices are
prone to both upward and downward jumps. This is why we found that both
volatility and directional motivated trades drive the bitcoin implied
volatility curve for calls as well as puts.

##  4 Methodology

To examine our net buying pressure hypotheses we first test the limits-to-
arbitrage versus learning hypotheses using the regression-based tests of
Bollen and Whaley, (2004), also used by Kang and Park, (2008). We then employ
the test of Chen and Wang, (2017) to distinguish between volatility-motivated
and directional-motivated demands.

First we fix notation. Let $j\in\\{C,P\\}$ and denote the change in ATM call
(resp. put) implied volatility from time $t-1$ to time $t$ by
$\Delta\sigma_{j,t}^{\mbox{\tiny ATM}}$. Here, as in all moneyness categories,
we obtain a single value for $\sigma_{C,t}^{\mbox{\tiny ATM}}$ by averaging
the implied volatilities over all ATM calls over each time interval $[t-1,t]$,
and similarly for $\sigma_{P,t}^{\mbox{\tiny ATM}}$. Now for
$k\in\left\\{\mbox{DOTM, OTM}\right\\}$, let $\Delta\sigma_{j,t}^{k}$ denote
the change from time $t-1$ to time $t$ in the average implied volatility of
all call (resp. put) options in moneyness category $k$. Let $r_{t}$ denote the
return of the Deribit bitcoin spot index and $v_{t}$ denote the aggregated
spot market volume from the exchanges in this index, both from time $t-1$ to
$t$. We proxy this with the aggregated USD volumes from the three largest spot
markets in the index, i.e. Bitstamp, Coinbase and Gemini. With this notation
and the buying pressure variables $A_{j,t}^{\mbox{\tiny ATM}}$ defined in (4),
the first two regressions of Bollen and Whaley, (2004) may be written:

$\displaystyle\Delta\sigma_{j,t}^{\mbox{\tiny ATM}}$
$\displaystyle=\alpha_{0j}+\alpha_{1j}r_{t}+\alpha_{2j}v_{t}+\alpha_{3j}A_{C,t}^{\mbox{\tiny
ATM}}+\alpha_{4j}A_{P,t}^{\mbox{\tiny
ATM}}+\alpha_{5j}\Delta\sigma_{j,{t-1}}^{\mbox{\tiny
ATM}}+\varepsilon_{t},\quad j\in\\{C,P\\}.$ (7)

Including the contemporaneous underlying return controls for leverage effects,
the trading volume controls for information flow effects, and the lagged
implied volatility captures mean-reversion so that significance of
$\alpha_{5C}$ and/or $\alpha_{5P}$ supports the limits-to-arbitrage
hypothesis.

If we cannot reject the hypothesis $\alpha_{3j}=\alpha_{4j}$, for either $j=C$
or $j=P$, then trading is strongly motivated by expectations about volatility;
this is because volatility traders have no reason to prefer ATM calls to ATM
puts or conversely. However, when $\alpha_{3C}$ and $\alpha_{4P}$ are both
significant and positive this does not necessarily imply that there is no
volatility learning, even if we do reject that $\alpha_{3j}=\alpha_{4j}$ for
either calls or puts. It only means that the idiosyncratic demand for ATM
calls is different from that for ATM puts. If we do find evidence in favour of
a learning hypothesis then, following Kang and Park, (2008) we can distinguish
which of volatility or directional learning is the dominant hypothesis by
running six further regressions of the form:

$\displaystyle\Delta\sigma_{j,t}^{k}$
$\displaystyle=\alpha_{0j}^{k}+\alpha_{1j}^{k}r_{t}+\alpha_{2j}^{k}v_{t}+\alpha_{3j}^{k}A_{j,t}^{k}+\alpha_{4j}^{k}A_{i,t}^{\mbox{\tiny
ATM}}+\alpha_{5j}^{k}\Delta\sigma_{j,{t-1}}^{k}+\varepsilon_{t}^{k},\quad
i,j\in\\{C,P\\}.$ (8)

for $k\in\left\\{\mbox{DOTM, OTM}\right\\}$. The regressors again include the
lagged change in implied volatility and its sign and significance
distinguishes limits-to-arbitrage from the dominant learning hypothesis, i.e.
that market makers learn from the prevalent type of trading, being volatility
motivated or directional motivated. In this case, changes in implied
volatility should be permanent and uncorrelated through time, hence that
$\alpha_{5j}=0$ should not be rejected. A significant estimate of
$\alpha_{4j}^{k}$ for both $k=\mbox{OTM}$ and $k=\mbox{DOTM}$ indicates that
demand for ATM options affects whole level of the implied volatility curve.
Under the directional-learning hypothesis informed traders would act
oppositely in calls and puts, so we expect significant values for
$\alpha_{3C}^{k}$ and/or $\alpha_{4P}^{k}$ with opposite signs, regardless of
moneyness $k$. The volatility-learning hypothesis predicts that
$\alpha_{4j}^{k}>\alpha_{3j}^{k}>0$ for calls and/or puts, because ATM options
have the greatest vega so traders should react most rapidly to ATM buying
pressures. We remark that it is also possible to have
$\alpha_{3j}^{k}>\alpha_{4j}^{k}>0$ under the volatility-learning hypothesis,
but this would only happen if the idiosyncratic volatility-motivated demand
for $k$-moneyness options dominate the volatility-motivated demand on ATM
options.

The methodology proposed by Kang and Park, (2008) can only assess which is the
dominating learning hypothesis, but the model proposed by Chen and Wang,
(2017) and later employed by Ryu et al., (2021) allows one to distinguish
between the two types of learning hypotheses by running regressions of the
form:

$\displaystyle\Delta\sigma_{j,t}^{k}$
$\displaystyle=\beta_{0j}^{k}+\beta_{1j}^{k}r_{t}+\beta_{2j}^{k}v_{t}+\beta_{3j}^{k}V_{t}^{k}+\beta_{4j}^{k}D_{j,t}^{k}+\beta_{5j}^{k}\Delta\sigma_{j,t-1}^{k}+\eta_{j,t}^{k},$
(9)

where $j\in\\{Call,Put\\}=\\{C,P\\}$ and $k\in\\{ATM,OTM,DOTM\\}$. The
parameters are similar to (8), except that we replace net buying pressure on
ATM options by two different testable components, i.e. directional-motivated
demand (5) and volatility-motivated demand (6). The size and significance of
$\beta_{3j}^{k}$ and $\beta_{4j}^{k}$ reveals which of the two learning
hypotheses predominates and the sign of $\beta_{4j}^{k}$ also indicates the
direction of the demand pressure on $k$-moneyness options of type $j$.

##  5 Empirical Results

As Table 2 shows, the trading volume on Deribit bitcoin options has increased
tremendously over time: from only 0.26 USD billion in 2017 to 102.96 USD
billion in January to July of 2021. This rapid increase in trading volume
supports our previous finding that the implied volatility curves for bitcoin
options have been converging to a shape very similar to that of the S&P 500
implied volatility curves – see Figure 1. This indicates that bitcoin options
prices since 2019 are likely to be more reliable and not distorted by stale
prices and low trading volumes. Our empirical results for 2017 and 2018
provide weak support for the limits-to-arbitrage hypothesis but do not show
any evidence of either directional or volatility learning. For brevity, we do
not present them here, but instead we focus on results for 2019, for 2020 and
for the first 7 months of 2021 – recalling that data were incomplete after
July 2021, since they were confined to short-term options only.

We use implied volatility and net buying pressure measures at the hourly
frequency but our results are robust to several other data frequencies, such
as 4 or 8 hours but not if we aggregate to the daily frequency. We aggregate
to hourly data because Deribit options are not as actively traded as major
equity index options, and also because a daily window is too wide to detect
informed trading in such a fast-changing and volatile market.131313The daily
results are available on request. Our main findings are that the limits-to-
arbitrage hypothesis is mainly supported by put options; that volatility
learning is more pronounced in 2019 and 2020; and that only directional
learning is supported in 2021 –- which is understandable due to the escalating
of bitcoin price during the 2021 sample.  Specifically, Bouoiyour et al.,
(2016), Goczek and Skliarov, (2019) and Brauneis et al., (2021) all show that
liquidity can be adversely affected by exogenous shocks such as large ‘whale’
bitcoin movements on blockchains, changes in investors sentiment recorded on
social media, or regulatory policy and economy policy uncertainties. The
effect of such shocks can sometimes be very short lived, because of the
extreme volatility of bitcoin. During the course of one day much information
flows into the market and the inventory managed by the market maker also
changes considerably, so we do not expect to identify the same buying pressure
effects on implied volatility at the daily frequency.

Table 7: The Test of Bollen and Whaley, (2004) for ATM, OTM, and DOTM Options

| Year |  | $\alpha_{0}$ | $\alpha_{1}$ | $\alpha_{2}$ | $\alpha_{3}$ | $\alpha_{4}$ | $\alpha_{5}$ | Nobs
---|---|---|---|---|---|---|---|---|---
|  |  | Panel A. ATM Options |
$\Delta\sigma^{\mbox{\tiny ATM}}_{C}$ | 2019 |  |  -0.27∗∗∗ | 6.609 |  0.067∗∗∗ |  3.072∗∗∗ | 1.264 |  -0.458∗∗∗ | 5868
2020 |  |  -0.58∗∗∗ |  -0.58∗∗∗ |  0.116∗∗∗ |  0.403∗∗ |  0.317∗ |  -0.426∗∗∗ | 8315
2021 |  |  -0.677∗∗∗ |  -31.985∗∗∗ |  0.041∗∗∗ |  0.2∗∗∗ | 0.015 |  -0.395∗∗∗ | 4192
$\Delta\sigma^{\mbox{\tiny ATM}}_{P}$ | 2019 |  |  -0.348∗∗∗ |  -21.161∗∗ |  0.073∗∗∗ | 0.015 |  7.594∗∗∗ |  -0.413∗∗∗ | 5034
2020 |  |  -0.608∗∗∗ |  -50.548∗∗∗ |  0.128∗∗∗ |  0.326∗ |  0.674∗∗∗ |  -0.399∗∗∗ | 7883
2021 |  |  -0.635∗∗∗ |  -46.709∗∗∗ |  0.038∗∗∗ |  0.127∗∗∗ |  -0.116∗ |  -0.397∗∗∗ | 4094
|  |  $i$ in (8) | Panel B. OTM Options |
$\Delta\sigma^{\mbox{\tiny OTM}}_{C}$ | 2019 | $Call$ |  -0.202∗∗∗ |  -16.439∗ |  0.07∗∗∗ |  4.188∗∗∗ | 0.925 |  -0.443∗∗∗ | 6548
$Put$ |  -0.194∗∗∗ | -12.071 |  0.068∗∗∗ |  4.25∗∗∗ |  1.5∗ |  -0.443∗∗∗ | 6548
2020 | $Call$ |  -0.569∗∗∗ | -13.064 |  0.122∗∗∗ |  1.19∗∗∗ | 0.284 |  -0.431∗∗∗ | 8581
$Put$ |  -0.563∗∗∗ | -8.446 |  0.122∗∗∗ |  1.298∗∗∗ |  0.421∗∗ |  -0.431∗∗∗ | 8581
2021 | $Call$ |  -0.717∗∗∗ |  -28.898∗∗∗ |  0.042∗∗∗ |  0.364∗∗∗ |  0.179∗∗∗ |  -0.386∗∗∗ | 4343
$Put$ |  -0.721∗∗∗ |  -25.284∗∗∗ |  0.043∗∗∗ |  0.406∗∗∗ | 0.058 |  -0.386∗∗∗ | 4343
$\Delta\sigma^{\mbox{\tiny OTM}}_{P}$ | 2019 | $Call$ |  -0.3∗∗∗ | 6.613 |  0.079∗∗∗ |  6.706∗∗∗ | 0.351 |  -0.444∗∗∗ | 6049
$Put$ |  -0.292∗∗∗ | 9.174 |  0.076∗∗∗ |  6.552∗∗∗ | 1.342 |  -0.444∗∗∗ | 6050
2020 | $Call$ |  -0.487∗∗∗ |  -72.922∗∗∗ |  0.105∗∗∗ |  0.972∗∗∗ |  0.385∗∗ |  -0.406∗∗∗ | 8446
$Put$ |  -0.487∗∗∗ |  -68.261∗∗∗ |  0.107∗∗∗ |  0.819∗∗∗ |  0.346∗ |  -0.406∗∗∗ | 8446
2021 | $Call$ |  -0.551∗∗∗ |  -28.553∗∗∗ |  0.034∗∗∗ |  0.255∗∗∗ |  0.143∗∗∗ |  -0.387∗∗∗ | 4293
$Put$ |  -0.544∗∗∗ |  -26.629∗∗∗ |  0.035∗∗∗ |  0.241∗∗∗ | -0.058 |  -0.388∗∗∗ | 4293
|  |  | Panel C. DOTM Options |
$\Delta\sigma^{\mbox{\tiny DOTM}}_{C}$ | 2019 | $Call$ |  -0.412∗∗∗ |  -26.902∗∗ |  0.109∗∗∗ |  23.144∗∗∗ | -0.76 |  -0.43∗∗∗ | 5040
$Put$ |  -0.404∗∗∗ |  -25.886∗∗ |  0.103∗∗∗ |  22.97∗∗∗ | 1.762 |  -0.43∗∗∗ | 5041
2020 | $Call$ |  -0.517∗∗∗ | -12.616 |  0.12∗∗∗ |  6.851∗∗∗ | 0.288 |  -0.466∗∗∗ | 7748
$Put$ |  -0.51∗∗∗ | -5.841 |  0.12∗∗∗ |  7.131∗∗∗ |  0.608∗∗ |  -0.466∗∗∗ | 7748
2021 | $Call$ |  -0.737∗∗∗ |  -23.409∗∗ |  0.047∗∗∗ |  2.098∗∗∗ |  0.13∗∗ |  -0.419∗∗∗ | 4214
$Put$ |  -0.729∗∗∗ |  -21.621∗∗ |  0.048∗∗∗ |  2.114∗∗∗ | -0.072 |  -0.42∗∗∗ | 4214
$\Delta\sigma^{\mbox{\tiny DOTM}}_{P}$ | 2019 | $Call$ |  -0.243∗ | 19.27 |  0.085∗∗∗ |  28.457∗∗∗ | -0.161 |  -0.422∗∗∗ | 4420
$Put$ | -0.223 | 23.283 |  0.077∗∗∗ |  28.134∗∗∗ |  3.139∗∗ |  -0.423∗∗∗ | 4421
2020 | $Call$ |  -0.503∗∗∗ |  -107.839∗∗∗ |  0.105∗∗∗ |  5.056∗∗∗ | 0.368 |  -0.42∗∗∗ | 7849
$Put$ |  -0.505∗∗∗ |  -103.141∗∗∗ |  0.107∗∗∗ |  4.926∗∗∗ | 0.123 |  -0.42∗∗∗ | 7849
2021 | $Call$ |  -0.513∗∗∗ |  -43.96∗∗∗ |  0.029∗∗∗ |  1.613∗∗∗ |  0.123∗ |  -0.406∗∗∗ | 4223
$Put$ |  -0.513∗∗∗ |  -41.181∗∗∗ |  0.03∗∗∗ |  1.592∗∗∗ | 0.01 |  -0.406∗∗∗ | 4223

  * •

Note. The top panel conducts regressions in (7) for ATM call and put options
from 2019 to 2021 and should be read as $\Delta\sigma_{call,t}^{\mbox{\tiny
ATM}}=\alpha_{0}+\alpha_{1}r_{t}+\alpha_{2}v_{t}+\alpha_{3}A_{call,t}^{\mbox{\tiny
ATM}}+\alpha_{4}A_{put,t}^{\mbox{\tiny
ATM}}+\alpha_{5}\Delta\sigma_{call,{t-1}}^{\mbox{\tiny ATM}}+\varepsilon_{t}.$
The middle and bottom panels report regressions in (8) for OTM and DOTM
options and are interpreted similarly. The limits-to-arbitrage hypothesis is
consistently supported by the highly significant coefficient $\alpha_{5}$. If
directional learning is supported, we would observe $\alpha_{3}>0$ and
$\alpha_{4}<0$ since traders would act oppositely on calls and puts whereas
volatility learning is more pronounced if both $\alpha_{3}$ and $\alpha_{4}$
are positive. ${}^{*},^{**},^{***}$ indicates 10%, 5% and 1% significance
levels respectively.

To differentiate limits-to-arbitrage from volatility/directional learning
hypotheses, we first run the Bollen and Whaley, (2004) test for ATM, OTM, and
DOTM option categories, examining the sign and magnitude of parameters
$\alpha_{3},\alpha_{4}$ and $\alpha_{5}$. Table 7 reports the results. Several
interesting facts are observed. First, in line with the findings of Bollen and
Whaley, (2004), Kang and Park, (2008) and Chen and Wang, (2017) for well-
developed option markets, the limits-to-arbitrage hypothesis is consistently
supported across moneyness categories. The lagged implied volatility
regression coefficient $\alpha_{5}$ estimates are negative and highly
significant with a decaying trend. For instance, in the ATM call options
category, the coefficient $\alpha_{5}$ decreases from $-0.458$ in 2019 to
$-0.395$ in 2021 that is roughly double the size of the corresponding
coefficient estimates found for well-developed index options markets. For
instance, a value of around -0.17 is reported for the S&P 500 options market
in Bollen and Whaley, (2004) and Chen and Wang, (2017) find a value of about
-0.23 for TAIEX index options. This shows that bitcoin options market makers
manage inventory less effectively than market makers for S&P 500 and TAIEX
options. However, as the bitcoin options market matures, we could expect
trading costs to diminish along with the heterogeneity of skills and knowledge
between bitcoin traders. As this maturing process continues in bitcoin markets
we expect the the magnitude of the limits-to-arbitrage coefficient
$\alpha_{5}$ to decrease continually.

Secondly, the estimate of the informational effect $\alpha_{2}$ is positive
and significant at 1%, for all moneyness categories in every year. Thus, spot
market trading volume has a positive effect on the change in implied
volatility, which is not a surprising as trading volume in bitcoin spot
markets is much larger than it is on Deribit options. Nevertheless, the
controlled leverage effect ($\alpha_{1}$) generally becomes more significant
over time, so Deribit is gradually attracting more participants to take highly
leveraged positions. Thirdly, for ATM options, the coefficients $\alpha_{3}$
and $\alpha_{4}$ are both positive, for calls and for puts, except for a
weakly significant $\alpha_{4P}<0$ in 2021 which is probably due to the surge
in bitcoin prices which rose from around 30,000 USD in January 2021 to above
63,000 USD in April 2021, then crashed back below 30,000 USD in July 2021.
Similarly, except for a weakly significant $\alpha_{4P}<0$ in 2021, we always
have $\alpha_{3}>\alpha_{4}>0$ for OTM and DOTM options. Hence, the estimate
of idiosyncratic net buy pressure $\alpha_{3}$ consistently drives the changes
in implied volatility levels of these options, and dominates the force of ATM
net buying pressure. This shows that although ATM options have the highest
volatility sensitivity (vega) they do not effectively drag the whole implied
volatility curve along OTM and DOTM categories. Taken together, we can infer
that volatility learning dominates directional learning. Additionally, the
gradually decreasing magnitudes of $\alpha_{3}$ and $\alpha_{4}$ year by year
indicates a maturing of the market where both option prices and IV levels are
more impacted by informed trading.

Table 8: The Test of Chen and Wang, (2017) for ATM, OTM, and DOTM Options

|  | $\beta_{0}$ | $\beta_{1}$ | $\beta_{2}$ | $\beta_{3}$ | $\beta_{4}$ | $\beta_{5}$ | Nobs |
---|---|---|---|---|---|---|---|---|---
|  |  | Panel A. ATM Options |
$\Delta\sigma_{C}^{\mbox{\tiny ATM}}$ | 2019 |  -0.27∗∗∗ | 6.609 |  0.067∗∗∗ |  4.336∗∗∗ | 1.808 |  -0.458∗∗∗ | 5868 |
2020 |  -0.58∗∗∗ | -13.841 |  0.116∗∗∗ |  0.72∗∗∗ | 0.086 |  -0.426∗∗∗ | 8315 |
2021 |  -0.677∗∗∗ |  -31.985∗∗∗ |  0.041∗∗∗ |  0.215∗∗∗ |  0.184∗∗ |  -0.395∗∗∗ | 4192 |
$\Delta\sigma_{P}^{\mbox{\tiny ATM}}$ | 2019 |  -0.348∗∗∗ |  -21.161∗∗ |  0.073∗∗∗ |  7.609∗∗∗ | 7.58 |  -0.413∗∗∗ | 5034 |
2020 |  -0.608∗∗∗ |  -50.548∗∗∗ |  0.128∗∗∗ |  1.0∗∗∗ | 0.349 |  -0.399∗∗∗ | 7883 |
2021 |  -0.635∗∗∗ |  -46.709∗∗∗ |  0.038∗∗∗ | 0.011 |  -0.243∗∗∗ |  -0.397∗∗∗ | 4094 |
|  |  | Panel B. OTM Options |
$\Delta\sigma_{C}^{\mbox{\tiny OTM}}$ | 2019 |  -0.188∗∗ | -9.277 |  0.067∗∗∗ |  6.594∗∗∗ | 1.685 |  -0.443∗∗∗ | 6550 |
2020 |  -0.564∗∗∗ | -8.791 |  0.122∗∗∗ |  1.599∗∗∗ |  0.982∗∗∗ |  -0.431∗∗∗ | 8581 |
2021 |  -0.715∗∗∗ |  -24.309∗∗∗ |  0.043∗∗∗ |  0.484∗∗∗ |  0.335∗∗∗ |  -0.386∗∗∗ | 4343 |
$\Delta\sigma_{P}^{\mbox{\tiny OTM}}$ | 2019 |  -0.299∗∗∗ | 6.379 |  0.079∗∗∗ |  7.135∗∗∗ |  6.22∗∗∗ |  -0.444∗∗∗ | 6051 |
2020 |  -0.482∗∗∗ |  -73.318∗∗∗ |  0.106∗∗∗ |  1.439∗∗∗ |  0.512∗∗ |  -0.407∗∗∗ | 8446 |
2021 |  -0.551∗∗∗ |  -30.256∗∗∗ |  0.034∗∗∗ |  0.426∗∗∗ | 0.063 |  -0.388∗∗∗ | 4293 |
|  |  | Panel C. DOTM Options |
$\Delta\sigma_{C}^{\mbox{\tiny DOTM}}$ | 2019 |  -0.408∗∗∗ |  -22.74∗ |  0.109∗∗∗ |  33.172∗∗∗ |  11.951∗ |  -0.43∗∗∗ | 5042 |
2020 |  -0.519∗∗∗ | -10.118 |  0.122∗∗∗ |  6.97∗∗∗ |  7.018∗∗∗ |  -0.466∗∗∗ | 7747 |
2021 |  -0.733∗∗∗ |  -18.559∗ |  0.048∗∗∗ |  2.493∗∗∗ |  1.756∗∗∗ |  -0.42∗∗∗ | 4214 |
$\Delta\sigma_{P}^{\mbox{\tiny DOTM}}$ | 2019 | -0.23 | 11.777 |  0.089∗∗∗ |  43.519∗∗∗ | 11.671 |  -0.424∗∗∗ | 4422 |
2020 |  -0.496∗∗∗ |  -105.627∗∗∗ |  0.106∗∗∗ |  6.521∗∗∗ |  3.878∗∗ |  -0.42∗∗∗ | 7848 |
2021 |  -0.505∗∗∗ |  -42.78∗∗∗ |  0.03∗∗∗ |  1.958∗∗∗ |  1.249∗∗ |  -0.407∗∗∗ | 4221 |

  * •

Note. This table reports regressions in (9) for ATM, OTM, and DOTM options.
For instance, in ATM options category, each row should be read as

$\Delta\sigma_{call,t}^{\mbox{\tiny ATM}}=\beta_{0}^{\mbox{\tiny
ATM}}+\beta_{1}^{\mbox{\tiny ATM}}r_{t}+\beta_{2}^{\mbox{\tiny
ATM}}v_{t}+\beta_{3}^{\mbox{\tiny ATM}}V_{t}^{\mbox{\tiny
ATM}}+\beta_{4}^{\mbox{\tiny ATM}}D_{t}^{\mbox{\tiny
ATM}}+\beta_{5}^{\mbox{\tiny ATM}}\Delta\sigma_{call,t-1}^{\mbox{\tiny
ATM}}+\eta_{t}^{\mbox{\tiny ATM}}.$

The ${}^{*},^{**},^{***}$ indicate 10%, 5% and 1% significance levels
respectively. Any significance of coefficients $\beta_{3}$ and $\beta_{4}$
demonstrates the existence of volatility and directional learning
respectively.

To investigate the possible co-existence of volatility and directional
learning we run the Chen and Wang, (2017) tests in (9) for ATM, OTM, and DOTM
options by turning off the channel of net-buying-pressure from ATM options.
The results are displayed in Table 8. Since for ATM, OTM and DOTM options the
estimate of $\beta_{3}$ is always greater than that of $\beta_{4}$,
volatility-motivated trades consistently dominate directional-motivated
trades. This finding is consistent with the results in Table 7 but contrasts
findings of previous studies on well-developed markets, where directional
learning is generally more pronounced than volatility learning, see Bollen and
Whaley, (2004), Kang and Park, (2008), Chen and Wang, (2017) and Ryu et al.,
(2021). Additionally, the sign, significance, and magnitude of $\beta_{4}$ for
directional trading varies across different moneyness categories, probably
because the bitcoin options market is still maturing. Similar findings about
net-buying-pressure varying for different option categories are presented by
Kang and Park, (2008) for KOSPI 200 index options and by Chen and Wang, (2017)
for TAIEX options.

Although the magnitudes of volatility and directional net buying pressures
differ, we could treat the ratio of $\beta_{3}/\beta_{4}$ in regressions (9)
as the relative strength of the two driving forces. For example, for the TAIEX
options market, Chen and Wang, (2017) find that the ratio
$\beta_{3}/\beta_{4}$ for OTM options is close to $2:5$, which implies that
the volatility trading effect is approximately 40% of the directional trading
effect for OTM options (see also the discussion of Table VII on Page 18 in
Chen and Wang, (2017)). Our results paint a different picture for bitcoin
options markets. We estimate a ratio $\beta_{3}/\beta_{4}$ about 3:2 for OTM
calls, which shows that the volatility learning effect is roughly 1.5 times
larger than the directional learning effect. So the evidence supporting the
learning hypothesis in bitcoin, is very different from the evidence from
established stock index options markets. That is, much more of the informed
trading in bitcoin options is about volatility rather than direction. Our
economic intuition behind this is that it is likely caused by, or could even
cause, the high volatility of bitcoin prices. Unfortunately, the regressions
we perform are not designed to detect the direction of causality, and that is
beyond the scope of this paper, but it would be an interesting subject for
further research.

However, it should be mentioned that only directional learning is evidenced by
ATM puts in 2021, and this is likely due to the bitcoin price bubble as
already noted above. In 2019 and 2020, both volatility and directional-
motivated demands drive OTM and DOTM implied volatility changes, while only
volatility information drives ATM option trades. The intuition here is that
informed traders with privileged volatility and directional information would
prefer trading cheaper OTM and DOTM options instead of more expensive ATM
options. This finding is in line with those for the KOSPI 200 options market
(Ryu et al.,, 2021) and the TAIEX index options market (Chen and Wang,, 2017).
But it contrasts the S&P 500 index options results of Bollen and Whaley,
(2004), the HSI index options results of Chan et al., (2004) and the KOSPI 200
index options results of Kang and Park, (2008). Finally, the limits-to-
arbitrage hypothesis is consistently supported, as previously demonstrated by
the regressions (7) and (8): the estimates of information flow and leverage
controls ($\beta_{1}$ and $\beta_{2}$) and of $\beta_{5}$ are all similar to
the values estimated for $\alpha_{1},\alpha_{2}$ and $\alpha_{5}$ in Bollen
and Whaley, (2004) test of Table 7.

Table 9: The Chen and Wang, (2017) Test for Options with Different Maturities:
2019

Model | Maturity | $\beta_{0}$ | $\beta_{1}$ | $\beta_{2}$ | $\beta_{3}$ | $\beta_{4}$ | $\beta_{5}$ | Nobs
---|---|---|---|---|---|---|---|---
|  | Panel A. ATM Options |
$\Delta\sigma_{C}^{\mbox{\tiny ATM}}$ | $[1,7]$ |  -0.596∗∗∗ | -7.087 |  0.136∗∗∗ |  6.855∗∗∗ |  5.322∗∗ |  -0.345∗∗∗ | 2662
$[8,21]$ |  -0.397∗∗∗ |  13.453∗ |  0.097∗∗∗ |  7.989∗∗∗ | -3.077 |  -0.279∗∗∗ | 2056
$\geq 22$ | -0.076 |  -28.118∗∗∗ |  0.029∗∗ | 1.857 | 2.12 |  -0.474∗∗∗ | 2453
$\Delta\sigma_{P}^{\mbox{\tiny ATM}}$ | $[1,7]$ |  -0.73∗∗∗ | 8.035 |  0.192∗∗∗ | 1.004 |  6.376∗ |  -0.374∗∗∗ | 2140
$[8,21]$ |  -0.549∗∗∗ |  -65.33∗∗∗ |  0.137∗∗∗ |  9.182∗∗∗ | 1.25 |  -0.391∗∗∗ | 1688
$\geq 22$ |  -0.258∗∗ |  -23.146∗∗ |  0.041∗∗∗ |  6.627∗∗∗ |  6.648∗∗∗ |  -0.371∗∗∗ | 1297
|  | Panel B. OTM Options |
$\Delta\sigma_{C}^{\mbox{\tiny OTM}}$ | $[1,7]$ |  -0.811∗∗∗ |  -48.143∗∗∗ |  0.203∗∗∗ |  22.084∗∗∗ | 3.808 |  -0.32∗∗∗ | 3253
$[8,21]$ |  -0.356∗∗∗ |  -15.165∗∗ |  0.09∗∗∗ |  8.202∗∗∗ |  3.634∗ |  -0.352∗∗∗ | 2509
$\geq 22$ | -0.07 | -3.898 |  0.04∗∗∗ |  7.561∗∗∗ | 3.148 |  -0.469∗∗∗ | 2974
$\Delta\sigma_{P}^{\mbox{\tiny OTM}}$ | $[1,7]$ |  -0.379∗∗ | 20.606 |  0.092∗∗∗ |  11.193∗∗∗ |  13.645∗∗∗ |  -0.226∗∗∗ | 2765
$[8,21]$ |  -0.365∗∗∗ | 11.133 |  0.085∗∗∗ |  8.962∗∗∗ |  5.624∗∗ |  -0.372∗∗∗ | 2170
$\geq 22$ |  -0.199∗∗ | -3.165 |  0.043∗∗∗ |  7.887∗∗∗ |  4.44∗∗ |  -0.525∗∗∗ | 2770
|  | Panel C. DOTM Options |
$\Delta\sigma_{C}^{\mbox{\tiny DOTM}}$ | $[1,7]$ |  -0.496∗∗ | 3.193 |  0.165∗∗∗ |  95.855∗∗∗ | 24.032 |  -0.345∗∗∗ | 1942
$[8,21]$ |  -0.475∗∗∗ |  -36.932∗∗∗ |  0.118∗∗∗ | 12.059 |  43.791∗∗∗ |  -0.371∗∗∗ | 1291
$\geq 22$ | -0.155 | -1.535 |  0.048∗∗∗ |  26.81∗∗∗ |  16.425∗ |  -0.418∗∗∗ | 1907
$\Delta\sigma_{P}^{\mbox{\tiny DOTM}}$ | $[1,7]$ |  -0.476∗ |  74.258∗∗∗ |  0.156∗∗∗ |  103.254∗∗∗ |  135.639∗∗∗ |  -0.267∗∗∗ | 1585
$[8,21]$ |  -0.412∗∗ | 5.732 |  0.106∗∗∗ |  52.84∗∗∗ | 18.197 |  -0.483∗∗∗ | 1011
$\geq 22$ | -0.219 | 18.968 |  0.061∗∗∗ | 10.825 |  26.332∗∗∗ |  -0.41∗∗∗ | 1367

  * •

Note. This table reports regressions in (9) for subsets of options by
maturity, using the terms ‘short-term’, ‘medium-term’, and ‘longer-term’ for
options with maturities lying in $[1,7]$, $[8,21]$ and $\geq 22$ days. The
${}^{*},^{**},^{***}$ indicate 10%, 5% and 1% significance levels
respectively.

Table 10: The Chen and Wang, (2017) Test for Options with Different
Maturities: 2020

Model | Maturity | $\beta_{0}$ | $\beta_{1}$ | $\beta_{2}$ | $\beta_{3}$ | $\beta_{4}$ | $\beta_{5}$ | Nobs
---|---|---|---|---|---|---|---|---
|  | Panel A. ATM Options |
$\Delta\sigma_{C}^{\mbox{\tiny ATM}}$ | $[1,7]$ |  -1.03∗∗∗ |  -28.32∗∗∗ |  0.201∗∗∗ |  1.717∗∗∗ | 0.779 |  -0.314∗∗∗ | 6834
$[8,21]$ |  -0.45∗∗∗ | -6.295 |  0.081∗∗∗ |  1.264∗∗∗ | 0.215 |  -0.267∗∗∗ | 4507
$\geq 22$ |  -0.173∗∗ | -1.605 |  0.032∗∗∗ | 0.338 | 0.009 |  -0.434∗∗∗ | 4756
$\Delta\sigma_{P}^{\mbox{\tiny ATM}}$ | $[1,7]$ |  -0.89∗∗∗ |  -96.113∗∗∗ |  0.182∗∗∗ |  1.98∗∗∗ |  1.046∗ |  -0.332∗∗∗ | 6148
$[8,21]$ |  -0.43∗∗∗ |  -103.303∗∗∗ |  0.091∗∗∗ |  1.916∗∗∗ | 0.56 |  -0.165∗∗∗ | 3386
$\geq 22$ |  -0.281∗∗ | -9.382 |  0.054∗∗∗ | 0.598 | 0.23 |  -0.353∗∗∗ | 2909
|  | Panel B. OTM Options |
$\Delta\sigma_{C}^{\mbox{\tiny OTM}}$ | $[1,7]$ |  -0.873∗∗∗ |  -37.728∗∗∗ |  0.187∗∗∗ |  5.168∗∗∗ |  2.942∗∗∗ |  -0.315∗∗∗ | 7408
$[8,21]$ |  -0.445∗∗∗ |  -25.821∗∗∗ |  0.084∗∗∗ |  1.801∗∗∗ |  1.504∗∗∗ |  -0.32∗∗∗ | 4862
$\geq 22$ | -0.215** |  -40.337∗∗∗ |  0.041∗∗∗ | 0.623 |  0.74∗ |  -0.437∗∗∗ | 5346
$\Delta\sigma_{P}^{\mbox{\tiny OTM}}$ | $[1,7]$ |  -0.905∗∗∗ |  -122.33∗∗∗ |  0.194∗∗∗ |  4.979∗∗∗ |  2.022∗∗∗ |  -0.314∗∗∗ | 7089
$[8,21]$ |  -0.401∗∗∗ |  -68.098∗∗∗ |  0.079∗∗∗ |  2.226∗∗∗ |  0.822∗∗ |  -0.306∗∗∗ | 4739
$\geq 22$ |  -0.211∗∗ |  -33.249∗∗∗ |  0.041∗∗∗ | 0.589 | 0.122 |  -0.444∗∗∗ | 5031
|  | Panel C. DOTM Options |
$\Delta\sigma_{C}^{\mbox{\tiny DOTM}}$ | $[1,7]$ |  -1.0∗∗∗ |  -70.308∗∗∗ |  0.196∗∗∗ |  24.28∗∗∗ |  17.258∗∗∗ |  -0.423∗∗∗ | 5452
$[8,21]$ |  -0.465∗∗∗ |  -59.095∗∗∗ |  0.084∗∗∗ |  9.26∗∗∗ |  7.233∗∗∗ |  -0.347∗∗∗ | 2839
$\geq 22$ | -0.113 |  -35.514∗∗∗ |  0.051∗∗∗ | 1.733 |  5.558∗∗∗ |  -0.449∗∗∗ | 3895
$\Delta\sigma_{P}^{\mbox{\tiny DOTM}}$ | $[1,7]$ |  -0.705∗∗∗ |  -135.8∗∗∗ |  0.16∗∗∗ |  20.181∗∗∗ |  14.017∗∗∗ |  -0.389∗∗∗ | 5704
$[8,21]$ |  -0.452∗∗∗ |  -70.164∗∗∗ |  0.08∗∗∗ |  11.789∗∗∗ |  6.511∗∗ |  -0.407∗∗∗ | 3132
$\geq 22$ | -0.163 |  -50.448∗∗∗ |  0.036∗∗∗ |  3.667∗ | 2.756 |  -0.464∗∗∗ | 3465

  * •

Note. This table reports regressions in (9) for subsets of options by
maturity, using the terms ‘short-term’, ‘medium-term’, and ‘longer-term’ for
options with maturities lying in $[1,7]$, $[8,21]$ and $\geq 22$ days. The
${}^{*},^{**},^{***}$ indicate 10%, 5% and 1% significance levels
respectively.

Table 11: The Chen and Wang, (2017) Test for Options with Different
Maturities: 2021

Model | Maturity | $\beta_{0}$ | $\beta_{1}$ | $\beta_{2}$ | $\beta_{3}$ | $\beta_{4}$ | $\beta_{5}$ | Nobs
---|---|---|---|---|---|---|---|---
|  | Panel A. ATM Options |
$\Delta\sigma_{C}^{\mbox{\tiny ATM}}$ | $[1,7]$ |  -1.206∗∗∗ |  -78.355∗∗∗ |  0.075∗∗∗ | 0.153 |  0.442∗∗ |  -0.316∗∗∗ | 3620
$[8,21]$ |  -0.563∗∗∗ |  -10.161∗ |  0.032∗∗∗ |  0.291∗∗∗ |  0.439∗∗∗ |  -0.22∗∗∗ | 2898
$\geq 22$ |  -0.218∗∗∗ | 6.894 |  0.013∗∗∗ | 0.121 |  0.286∗∗∗ |  -0.406∗∗∗ | 3332
$\Delta\sigma_{P}^{\mbox{\tiny ATM}}$ | $[1,7]$ |  -0.936∗∗∗ |  -70.334∗∗∗ |  0.059∗∗∗ | -0.222 |  -0.823∗∗∗ |  -0.295∗∗∗ | 3324
$[8,21]$ |  -0.711∗∗∗ |  -37.339∗∗∗ |  0.04∗∗∗ |  0.319∗∗∗ | -0.098 |  -0.172∗∗∗ | 2506
$\geq 22$ |  -0.358∗∗ | -14.85 |  0.02∗∗∗ | -0.256 |  -0.506∗∗∗ |  -0.434∗∗∗ | 2552
|  | Panel B. OTM Options |
$\Delta\sigma_{C}^{\mbox{\tiny OTM}}$ | $[1,7]$ |  -1.113∗∗∗ |  -71.348∗∗∗ |  0.072∗∗∗ |  0.9∗∗∗ |  0.695∗∗∗ |  -0.273∗∗∗ | 3996
$[8,21]$ |  -0.654∗∗∗ | -7.892 |  0.036∗∗∗ |  0.66∗∗∗ |  0.345∗∗∗ |  -0.265∗∗∗ | 3400
$\geq 22$ |  -0.245∗∗∗ | -5.492 |  0.015∗∗∗ |  0.301∗∗ |  0.3∗∗ |  -0.402∗∗∗ | 3592
$\Delta\sigma_{P}^{\mbox{\tiny OTM}}$ | $[1,7]$ |  -0.995∗∗∗ |  -115.481∗∗∗ |  0.068∗∗∗ |  1.145∗∗∗ |  0.663∗∗∗ |  -0.288∗∗∗ | 3911
$[8,21]$ |  -0.552∗∗∗ |  -45.935∗∗∗ |  0.03∗∗∗ |  0.468∗∗∗ | -0.044 |  -0.344∗∗∗ | 3317
$\geq 22$ |  -0.323∗∗∗ | 0.47 |  0.017∗∗∗ | 0.287 | 0.016 |  -0.465∗∗∗ | 3565
|  | Panel C. DOTM Options |
$\Delta\sigma_{C}^{\mbox{\tiny DOTM}}$ | $[1,7]$ |  -1.293∗∗∗ |  -52.329∗∗∗ |  0.078∗∗∗ |  4.582∗∗∗ |  5.204∗∗∗ |  -0.399∗∗∗ | 3417
$[8,21]$ |  -0.714∗∗∗ | -5.671 |  0.041∗∗∗ |  3.454∗∗∗ |  2.808∗∗∗ |  -0.352∗∗∗ | 2563
$\geq 22$ |  -0.316∗∗∗ | -8.414 |  0.02∗∗∗ |  2.698∗∗∗ |  1.212∗ |  -0.473∗∗∗ | 2922
$\Delta\sigma_{P}^{\mbox{\tiny DOTM}}$ | $[1,7]$ |  -0.809∗∗∗ |  -139.774∗∗∗ |  0.061∗∗∗ |  5.505∗∗∗ |  2.618∗∗ |  -0.372∗∗∗ | 3438
$[8,21]$ |  -0.57∗∗∗ |  -38.043∗∗∗ |  0.032∗∗∗ |  1.437∗ |  3.195∗∗∗ |  -0.376∗∗∗ | 2634
$\geq 22$ | -0.315 | -4.755 | 0.01 |  2.882∗∗ | 1.477 |  -0.459∗∗∗ | 2800

  * •

Note. This table reports regressions in (9) for subsets of options by
maturity, using the terms ‘short-term’, ‘medium-term’, and ‘longer-term’ for
options with maturities lying in $[1,7]$, $[8,21]$ and $\geq 22$ days. The
${}^{*},^{**},^{***}$ indicate 10%, 5% and 1% significance levels
respectively.

Next we apply the methodology of Chen and Wang, (2017) to subsets of options
by maturity, using the terms ‘short-term’, ‘medium-term’, and ‘longer-term’
for options with maturities lying in $[1,7]$, $[8,21]$ and $\geq 22$ days. In
general, we find that the volatility-informed traders prefer short-term and
medium-term options. In 2020, trading on longer-term ATM options only supports
the limits-to-arbitrage hypothesis, whereas it is directional trading that
dominates prices of the longer-term OTM calls, and volatility information that
drives the prices of longer-term DOTM puts. Although more directional trading
emerges in longer-term options during 2021, less informed trading is present
in longer-term options overall, than in short and medium-term options.

The tick-level data also allows investigation of time-of-day effects, for
which there are conflicting results from previous research. For instance, Jain
et al., (2019) found bitcoin spot trading volume is higher on centralised
exchanges during their local working hours and that there was substantial
weekend trading, both reflecting high retail participation. However, Alexander
et al., 2021b  found that most volatility transmission between bitcoin
perpetual swaps and spot markets occurs during US and Asian trading times.
Both these papers focused on spot and futures only. Our next results are the
first to investigate time-of-day effects of buying pressures in bitcoin
options markets.

Table 12: Net Buying Volume and Net Buying Pressure by Time of Day

Time of Day (UTC) | 00:00 – 08:00 | 08:00 – 16:00 | 16:00 – 24:00
---|---|---|---
Year | Call | Put | Call | Put | Call | Put
| Panel A. Net Buying Pressure
2017 | 8.45 | 0.05 | 13.87 | -1.15 | 13.66 | 1.69
2018 | -14.98 | -8.89 | 6.68 | 9.33 | 13.52 | 7.02
2019 | 40.03 | 35.53 | 60.42 | 18.20 | 55.49 | 3.56
2020 | 331.96 | -134.49 | 804.47 | 473.04 | 118.93 | -358.11
2021 | 1854.06 | 459.91 | 1856.20 | 1070.60 | 448.06 | 42.02
| Panel B. Direction Net Buying Pressure for Calls
2017 | 4.20 | 7.51 | 5.98
2018 | -3.05 | -1.32 | 3.25
2019 | 2.25 | 21.11 | 25.96
2020 | 233.23 | 165.72 | 238.52
2021 | 697.08 | 396.61 | 203.02
| Panel C. Volatility Net Buying Pressure
2017 | 4.25 | 6.36 | 7.68
2018 | -11.93 | 8.00 | 10.27
2019 | 37.78 | 39.31 | 29.53
2020 | 98.73 | 638.75 | -119.59
2021 | 1156.99 | 1467.21 | 245.04

  * •

Note. Panel A: Average of the 8-hour net buying pressure measures for calls
and puts over different years in three time zones: 00:00 – 08:00 (Asia), 08:00
– 16:00 (Europe) and 16:00 – 00:00 (US). Panels B and C disaggregate of the
net buying pressure shown in Panel A into directional-motivated and
volatility-motivated net buying pressure. For calls, the entry in Panel A is
the sum of the corresponding entries in Panels B and C. For puts, the entry in
Panel A is the difference between the corresponding entries in Panels C and B.

Table 12 reports the net buying pressure, and the directional- and volatility-
motivated buying pressures by the time-of-day, where we group results into
8-hour time slots and take the average during each year. The time slots of
00:00 – 08:00, 08:00 – 16:00, and 16:00 – 24:00 UTC are chosen because they
roughly correspond to Asian, European and US trading hours, respectively. It
is really noticeable that option trader’s net buying pressure is much lower
during US trading times. Also distinct time-of-day pattern emerges in 2020 and
2021, where directional-motivated demand is greatest during Asian trading
times and volatility-motivated demand most evident during European trading
times. But further tests, reported in Table 13, show that volatility-motivated
demand, mainly driven by ATM options, is greatest during US and Asian trading
times. This finding is also supported by the volatility-transmission results
of Alexander et al., 2021b . So although Table 12 shows that the greatest
volatility-motivated demand occurs during European trading times, the
information content of this demand is relatively low. Another take-away from
the OTM and DOTM results in Table 13 is that directional learning is only
supported during Asian and US trading times.

Table 13:  The Time-of-Day Effect of Volatility and Directional Learning

| UTC Time | $\beta_{0}$ | $\beta_{1}$ | $\beta_{2}$ | $\beta_{3}$ | $\beta_{4}$ | $\beta_{5}$
---|---|---|---|---|---|---|---
|  | Panel A. ATM Options
$\Delta\sigma_{C}^{\tiny\mbox{ATM}}$ | $(0,8]$ |  -4.367∗∗∗ | -9.196 |  0.057∗∗∗ |  0.417∗ | 0.222 |  -0.094∗
$(8,16]$ | 0.636 | 1.099 |  0.03∗∗∗ | 0.327 | -0.561 |  -0.17∗∗∗
$(16,24]$ |  -1.301∗∗∗ |  -53.767∗∗∗ |  0.044∗∗∗ |  0.74∗∗ | 0.461 |  -0.112∗∗
$\Delta\sigma_{P}^{\tiny\mbox{ATM}}$ | $(0,8]$ |  -4.937∗∗∗ |  -74.652∗∗∗ |  0.066∗∗∗ | 0.268 | -0.005 | -0.001
$(8,16]$ | 0.682 | 7.111 |  0.039∗∗∗ | 0.329 | 0.581 |  -0.191∗∗∗
$(16,24]$ |  -1.907∗∗∗ |  -163.991∗∗∗ |  0.081∗∗∗ |  1.177∗∗∗ | -0.28 |  -0.255∗∗∗
|  | Panel B. OTM Options
$\Delta\sigma_{C}^{\tiny\mbox{OTM}}$ | $(0,8]$ |  -3.469∗∗∗ | -4.27 |  0.049∗∗∗ |  0.76∗∗∗ |  0.959∗∗∗ | -0.069
$(8,16]$ |  1.186∗∗∗ |  25.891∗ |  0.03∗∗∗ | 0.001 | 0.242 | 0.002
$(16,24]$ |  -2.278∗∗∗ |  -79.752∗∗∗ |  0.069∗∗∗ |  2.044∗∗∗ |  1.697∗∗∗ |  -0.137∗∗
$\Delta\sigma_{P}^{\tiny\mbox{OTM}}$ | $(0,8]$ |  -3.535∗∗∗ |  -85.011∗∗∗ |  0.051∗∗∗ |  0.886∗∗∗ | -0.231 | 0.055
$(8,16]$ | 0.471 |  -57.316∗∗∗ |  0.043∗∗∗ | 0.264 | 0.123 |  -0.159∗∗∗
$(16,24]$ |  -2.165∗∗∗ |  -131.82∗∗∗ |  0.077∗∗∗ |  1.852∗∗∗ |  -0.85∗∗∗ |  -0.144∗∗∗
|  | Panel C. DOTM Options
$\Delta\sigma_{C}^{\tiny\mbox{DOTM}}$ | $(0,8]$ |  -3.891∗∗∗ | -4.825 |  0.048∗∗∗ |  3.802∗ |  6.51∗∗∗ |  -0.294∗∗∗
$(8,16]$ | 0.415 | 18.39 |  0.041∗∗∗ |  6.021∗∗∗ | 0.596 | -0.024
$(16,24]$ |  -1.287∗∗ |  -92.179∗∗∗ |  0.083∗∗∗ |  8.909∗∗∗ |  9.339∗∗∗ |  -0.257∗∗∗
$\Delta\sigma_{P}^{\tiny\mbox{DOTM}}$ | $(0,8]$ |  -4.127∗∗∗ |  -188.93∗∗∗ |  0.05∗∗∗ |  5.759∗∗∗ | -2.15 |  -0.281∗∗∗
$(8,16]$ | 0.328 |  -88.713∗∗∗ |  0.035∗∗∗ |  5.088∗∗∗ | -0.381 |  -0.112∗∗∗
$(16,24]$ | -1.033 |  -309.699∗∗∗ |  0.104∗∗∗ | 5.362 |  -6.475∗ |  -0.368∗∗∗

  * •

Note. Table 12 shows the time-of-day pattern only really emerged after 2020.
Therefore, in this table we run the regressions in (9) using data from 2020
and 2021 only. The ${}^{*},^{**},^{***}$ indicate 10%, 5% and 1% significance
levels respectively.

##  6 Conclusion

Compared with the well-developed S&P 500 options market which is also severely
regulated, we found numerous differences in the bitcoin options market which
is dominated by the ‘self-regulated’ exchange, Deribit. S&P 500 options
implied volatility curves have exhibited a marked ‘skew’ for decades, and the
ATM volatility has been around 20% most of the time. By contrast, the bitcoin
implied volatility curve is much higher, with ATM volatility often around 100%
but the level is also very variable, and the curve is much flatter and more
symmetric than the S&P 500 ‘skew’ shape. All these differences point to quite
different data generation processes for the underlying prices. For instance,
the features we have documented in bitcoin implied volatilities indicate that
the stochastic volatility models driving bitcoin prices should include
positive as well as negative jumps, which are correlated with the variance
process.

However, the focus of our study in this paper is not on option pricing but on
the information we can derive from trading patterns in bitcoin options, by
modelling their implied volatilities. The existence of informed trading is
clearly supported by our regressions of returns, and realised volatility and
implied volatility on their own lag and the lagged trading volume of Deribit
bitcoin options. We examine the limits-to-arbitrage hypothesis for market
maker’s supply, and the volatility- and directional-motivated demand-side
effects on hourly changes in the implied volatility of Deribit bitcoin
options, using different types of net-buying-pressure metrics. By contrast
with previous results on well-developed stock and index options markets, our
results show that not only limits-to-arbitrage constraints but also
volatility-informed demand are the main driving forces behind ATM options,
although the net buying pressure from ATM options does not appear to drag the
whole implied volatility curve along when ATM volatility changes. Deribit
trading volumes have increased enormously during the last few years and market
makers are using these options to manage order imbalance and inventory more
effectively as the market matures. Also most traders are motivated to pursue
volatility information for the purpose of hedging, arbitraging and
speculating.

The bitcoin market is highly volatile and no consensus on the fundamentals of
bitcoin prices is widely acknowledged, so it is extremely difficult for most
traders to exploit advanced information about the direction of bitcoin price
movement. We find that directional learning, as well as volatility learning,
is supported by our results for OTM and DOTM options which are much less
expensive than ATM options. Directional learning effects are more pronounced
during 2021, even being present in ATM put options. We attribute this to the
price bubble and crash which may have been precipitated by the behaviour of a
few large highly-informed traders.

Further refinements of our tests assess time-to-maturity and time-of-day
effects. We find that volatility-informed trading dominates demand pressures
on short-term and medium-term options. Although more directional trading is
apparent in longer-term options during 2021, overall they encompass less
informed trades than short- and medium-term options. The time-of-day patterns
indicate that net buying pressure grew rapidly during 2020 and 2021, that
directional pressure is strongest during Asian trading times and volatility
pressure is strongest during European times. As in traditional option markets
we find strong evidence of market makers managing inventory under limits-to-
arbitrage. However, in contrast with traditional markets, we also find that
bitcoin market makers adjust prices using information from both directional
and volatility motivated trades, especially by observing demand pressures
during Asian and US trading times.

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