Question #64

Reading: Reading 31 Valuation of Contingent Claims

PDF File: Reading 31 Valuation of Contingent Claims.pdf

Page: 30

Status: Unattempted

Part of Context Group: Q63-64
Shared Context
- Which of the following best describes how a payer swap could be replicated using interest rate swaptions? A) The swap can be replicated by selling a payer swaption and buying a receiver swaption at the same strike. B) The swap can be replicated by buying a payer swaption and selling a receiver swaption at the same strike. C) The swap can be replicated by buying a payer swaption and selling a receiver swaption at different strikes.
Question
Which of the following comments relating to the Black model valuation of a swaption is the most accurate?
Answer Choices:
A. SFR in the formula identified by Lucy is the market swap fixed rate at the expiration of the swaption
B. N(d2) is likely to be greater than N(d1)
C. A payer swaption will only be exercised in the market swap fixed rate at expiry is greater than the swaption’s strike price
Explanation
SFR in the Black formula represents the current market swap fixed rate not the fixed rate at expiration. Both the Black and BSM formulas use the current price of the underlying asset. The Black formula, like BSM computes the expected value of what you will receive less the present value of what you will pay given assumptions such as volatility. N(d2) = only considers probability that the option is exercised (i.e., the probability of the market SFR being greater than the strike at expiration). N(d1) has to adjust the current SFR to the expected SFR at expiration given that the option will only be exercised if the market SFR > strike rate. The result is that in the Black and BSM formulas that N(d1) is slightly higher than N(d2). A payer swaption will only be exercised if the strike rate is lower than the market rate on a pay fixed swap at expiry. When a swaption is exercised the holder will pay fixed at the strike price and receive floating. This will be attractive when the fixed rate on a pay fixed swap in the market is higher. The floating payments can be ignored as the rate on swaption when exercised and the rate on a new swap at expiry would be identical.
Actions
Practice Flashcards