Question #56

A receiver swaption gives its owner the right to receive fixed, the writer has an obligation to pay fixed. (Module 31.6, LOS 31.j) Nathan Detroit, a speculator, has come to you for technical advice regarding the pricing of swaps. He hopes to make big money in the swaps market from the exploitation of pricing discrepancies, but lacks an understanding of the principles underlying the pricing of swaps. He asks you to consider a two-year, fixed-for-fixed, currency swap with semiannual payments. The domestic currency is the U.S. dollar and the foreign currency is the U.K. pound. The current exchange rate is $1.60 per pound. You forecast that the exchange rate would be $1.41 on the first settlement date. The notional principal of the swap is set at $10 million. The USD and £ term structure are shown in Exhibits 1 and 2 below. Exhibit 1: Current USD Term Structure Number of Days MRR Present Value Factor 180 0.0585 0.9716 360 0.0605 0.9430 540 0.0596 0.9179 720 0.0665 0.8826 Exhibit 2: Current £ Term Structure Number of Days MRR Present Value Factor 180 0.0493 0.9759 360 0.0450 0.9569 540 0.0519 0.9278 720 0.0551 0.9007 Detroit has heard about the European put-call parity theorem and believes a synthetic call can be created through the use of a European put with the same strike as the call, a zero coupon bond with a face value equal to the strike price of the put and an underlying asset relating to the put and the call. Detroit makes two comments regarding the BSM model and the Black model as follows: Comment 1: N(d1) in the BSM is the probability that the option will expire in the money. Comment 2: The probability that a receiver swaption will expire in the money is N(–d2).