We will derive a two-state call option value in this problem. Data: S 0 = 150; X

Question

We will derive a two-state call option value in this problem. Data: S0 = 150; X = 160; 1 + r = 1.1. The two possibilities for ST are 180 and 100.

a. The range of S is 80 while that of C is 20 across the two states. What is the hedge ratio of the call? (Round your answer to 2 decimal places.)

Hedge ratio            

b. Calculate the value of a call option on the stock with an exercise price of 160. (Do not use continuous compounding to calculate the present value of X in this example, because the interest rate is quoted as an effective per-period rate.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Call value            $

Explanation / Answer

a). Solution :- Hedge ratio = (20 - 0) / (180 - 100)

= 20 / 80

= 0.25

Conclusion :- Hedge ratio of call option = 0.25

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