Consider again the risk neutral tree for interest rates in Table 12.11, where there is equal risk neutral probability to move up or down the tree.

(a) Compute the tree for an American swaption with maturity i = 3 and strike rate c = 5.25%.
(b) Consider now a callable bond with maturity i - 3, principal = 100, and annual coupon rate = 5.25%.
(c) An investor is long the callable bond priced in the previous exercise, and is worried about prepayment risk. Can you suggest how the investor can employ an American swaption to hedge against prepayment risk? Assume the investor is not worried about interest rate risk.
(d) Assume that the investor in the callable bond is instead worried about interest rate risk. Can you suggest a hedging strategy that would cover the investor against changes in the interest rates?

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i-0 i-1 i-2 r2.uu-6% rı 5.5% 5% r2.ud-5% rld 4.7% ry.dd 4.5% Maturity (Years) Price Yield 0.5 し0 1.74 2.13 2.62 3.04 2.0 2.5 3.0 3.5 4.0 4.5 5.0 99.1338 97.8925 96.1462 94.1011 91.7136 89.2258 86.8142 84.5016 82.1848 79.7718 3,80 4.04 4.21 4.36