We will derive a two-state call option value in this problem. Data: S 0 = 120; X

Question

We will derive a two-state call option value in this problem. Data: S0 = 120; X = 100; 1 + r = 1.1. The two possibilities for ST are 140 and 90.

a. The range of S is 50 while that of C is 40 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 100. (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). Hedge Ratio for the call = (Cu - Cd) / (uS0 - dS0 ) = (40 - 0) / (140 - 90) = 0.8

b).

Present Value = $360 / 1.1 =$327.273

Portfolio cost = 4S– 5C

$327.273 = $480 - 5C

5C = $152.727

C = $30.55

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