text: abstract
  we show that, for the purpose of pricing swaptions, the swap rate and the corresponding forward rates can be
  considered lognormal under a single martingale measure. swaptions can then be priced as options on a basket of
  lognormal assets and an approximation formula is derived for such options. this formula is centered around a blackscholes price with an appropriate volatility, plus a correction term that can be interpreted as the expected tracking
  error. the calibration problem can then be solved very efficiently using semidefinite programming.
  keywords: semidefinite programming, libor market model, calibration, basket options.