Question #61

- How many of Nathan's comments are correct? A) Neither comment is correct. B) Only one statement is correct. C) Both statements are correct. Lucy Wang is the Chief Financial Officer of Sam Corporation. Sam Corporation has floating rate liabilities and wants to hedge against the possibility of rising interest rates. Wang is looking into using swaptions to hedge against interest rate risk. The board of Sam Corporation are not familiar with both swaps and swaptions. To explain the characteristics of swaps, Wang explains to the board that swaps are similar to interest rate options. Wang decides to use a swaption to hedge against interest rate risk. She knows that there are two types of swaptions just like there are both call and put options, and that the cash flows on swaps can be replicated using swaptions. Lucy is very interested in the application of the Black model in pricing swaptions. After a quick search online she has found the following: pay = (AP)PVA ⎡⎣SFR × N(d1) – X × N(d2 )⎤⎦× NP where: pay = value of the payer swaption AP = 1 / number of settlement periods per year in the underlying swap X = exercise rate specified in the swaption NP = notional principal Lucy is confused regarding what the notation PVA stands for and states: "There are multiple payoffs on a swaption, each being the difference between the market swap rate at expiration and the exercise rate at each settlement date, over the swaps life. Given each payoff arises at a different point in time over the swaps life, each must be discounted back to the current period using discount rate specific to when it occurs. The PVA therefore must be an annuity factor summing all these specific discount rates." Lucy also states: "A payer swaption is right to enter a swap with a fixed rate equal to the strike price at the options maturity. The payoffs will therefore represent the difference in the swaptions strike price and the fixed market swap rate at the time of option expiry. Given we are comparing the payer swap underlying the swaption, versus the market rate of a payer swap at the option maturity, the floating payments can be ignored as they will offset. This is why the Black model only includes values for the current market swap fixed rate and fixed rate of the swap underlying the swaption (i.e., the strike)."