Swaptions with a smile

Swaptions are among the most popular instruments in thefixed-income option market. These are options to entera floating versus fixed forward starting interest rate swapat a predetermined fixed rate, known as a strike coupon.Standard market practice is to price these instruments byapplying the Black-Scholes (1973) formula to the yield ofthe underlying forward par swap. An option to enter a forward startingswap is worth the present value of 1 basis point annuity times the Black-Scholes price function of the forward par yield, the strike swap couponand the annualised volatility of the yield (Jamshidian, 1997).1 While thereis no ambiguity about the value of the annuity or the forward yield, differentmarket participants may have a different view on the volatility ofthe yield.2 This variable of the option pricing formula is the central themeof this article.

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