We will derive a two-state call option value in this problem. Data: S 0 = 200; X

Question

We will derive a two-state call option value in this problem. Data: S0 = 200; X = 210; 1 + r = 1.1. The two possibilities for ST are 230 and 180.

a. The range of S is 50 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 210. (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) Calculation of Hedge Ratio: Difference in payoff/Difference in MP Today MP=200 Possible market Price at T point of time S(T)=230 and 180 Strike Price(X)=210 Rate of Return=1+r=1.1 r=.1 ; 10% Calculation of Probabilities (Risk Neutral Method) Spot price(1+r)^n-Lower price/High Price-Low Price ; r=rate of return per period n=no of period 200(1+10%)^1-180/230-180 200*((1+10%)^1))-180/(230-180) P(high Price)=80% P(low Price) (100-80%)=20% Strike Price Market Price Action Payoff Probabilities Expected Payoff (MP-Sp) (Payoff * Prob.) 210 230 Exercise,as MP>Sp 20 80.00%             16.00 210 180 Lapse,as sp

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