Assume the structure of bond prices in Example 11.5 (Figure 11.10). Consider a coupon bond maturing at time 2 with face value F = 100 and coupons C = 1 payable at each step. Find the price of an American call option expiring at time 2 with strike price X = 101.30. (Include the coupon in the bond

Question

Assume the structure of bond prices in Example 11.5 (Figure 11.10). Consider a coupon bond maturing at time 2 with face value F = 100 and coupons C = 1 payable at each step. Find the price of an American call option expiring at time 2 with strike price X = 101.30. (Include the coupon in the bond price at each step.)

Accepted Answer

At time 2 the option is worthless. At time 1 we evaluate the bond prices by
adding the coupon to the discounted final payment of 101.00 at the appropriate (monthly) money market rate: 0.521% in the up state and 0.874% in the down state. The results are 101.4748 and 101.1213, respectively. The option can be exercised at that time in the up state, so the cash flow is 0.1748 and 0, respectively. Expectation with respect to the risk-neutral probabilities of the discounted cash flow gives the initial value 0.06598 of the option.

Question 11.11: Assume the structure of bond prices in Example 11.5 (Figure ...

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