We will derive a two-state call option value in this problem. Data: S 0 = 250; X

Question

We will derive a two-state call option value in this problem. Data: S0 = 250; X = 260; 1 + r = 1.1. The two possibilities for ST are 280 and 180.

a. The range of S is 100 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 260. (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) uS0 = 280

dS0 = 180

Range of C is 20 , so when ST = 280, C= 20 and when ST = 180 , C= 0

Hedge ratio = Cu - Cd /uS0 - dS0 = 20-0 / 280-180 = 20/100 = 0.2

b) Value of call option = Market price - Exercise price = $250 - $260/1.1 = $13.63

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