Let (R, P) be the value of a European receiver, payer swaption with the same expiry, swap

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Let $R, P$ be the value of a European receiver, payer swaption with the same expiry, swap term, and strike $K$.

(a) Let $S$ be the value to the receiver of the underlying swap with fixed rate $K$. Prove put-call parity for European-style swaptions: $R-P=S$.

(b) Using Table 7.3, calculate the value to the fixed-rate receiver of a \$1M 1 year into 2-year forward swap with semiannual fixed rate of $4 \%$ per annum.

(c) Using the results of Example 3, show that put-call parity holds.

Table 7.3

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Mathematical Techniques In Finance An Introduction Wiley Finance

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1st Edition

Authors: Amir Sadr

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Question Posted: Feb 27, 2024 03:11 AM

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Let (R, P) be the value of a European receiver, payer swaption with the same expiry, swap

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T (years) 0 0.5 1 1.5 2 2.5 3 D(T) 1 0.98 0.96 0.94 0.92 0.90 0.88 f([T, T + 6m]) 4.082% 4.167% 4.255% 4.348% 4.444% 4.545% S(T) 4.082% 4.124% 4.167% 4.211% 4.255% 4.301%

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Mathematical Techniques In Finance An Introduction Wiley Finance

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