Data: S0 = 120; X= 138; 1 + r= 1.15. The two possibilities for ST are 150 and 10

Question

Data: S0 = 120; X= 138; 1 + r= 1.15. The two possibilities for ST are 150 and 102. 1. The range of S is 48, while that of C is 12 across the two states. What is the hedge ratio of the call? (Round your answer to 2 decimal places.) Hedge ratio 2. Calculate the value of a call option on the stock with an exercise price of $138. (Do not use continuous compounding to calculate the present value of X in this example because we are using a two-state model here, not a continuous-time Black-Scholes model.) (Round your answer to 2 decimal places. Omit the "S" sign in your response.) Call value

Explanation / Answer

S = 120, Su = 150, Sd = 102, X = 138, Cu = 150 - 138 = 12, Cd = 0

R = 1 + r = 1.15

Hedge ratio = (Cu - Cd)/(Su - Sd) = (12 - 0)/(150 - 102) = 12/48 = ¼ = 0.25

Risk-neutral probability: p = (R - d)/(u - d)

p = (1.15 - 102/120)/(150/120 - 102/120) = 0.75

1 - p = 0.25

C = [p*Cu + (1 - p)*Cd]/R = (0.75*12 + 0.25*0)/1.15 = 7.8261

Call value = $7.83

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