We will derive a two-state put option value in this problem. Data: S 0 = 110; X

Question

We will derive a two-state put option value in this problem. Data: S0 = 110; X = 120; 1 + r = 1.1. The two possibilities for ST are 140 and 100.

The range of S is 40 while that of P is 20 across the two states. What is the hedge ratio of the call?

Calculate the value of a call option on the stock with an exercise price of 120. (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.)

We will derive a two-state put option value in this problem. Data: S0 = 110; X = 120; 1 + r = 1.1. The two possibilities for ST are 140 and 100.

Explanation / Answer

Ans) Put Option SP0 = 110 Exercise Price EP = 120 R = 1.1 FP1 = 140 FP2 = 100 FP1 FP2 Future Spot Price 140 100 Postion of Expiry Date (In Comparsion with Exercise Price) In the Money Out of Money Action on Expiry Date Lapse Exercise Value of Option on Expiry (Future Spot Price Less Execise Price) 30 0 (140-110) Option Delta = Change in Value of Option/ Change in Future Spot Price = (30-0) / (140-100) = 30/40 = 0.75 B) Compution of Amount to be invested at risk free rate = Present Value of Lower Bond of Future Spot Price i.e FP2 Note:- In this Problem the he already applied for compund interest. Hence, Present value of Lower Bond of future spot Price = $                   100 C) Value of Call © = Option Delta * Current Stock Price Less Amount to be invested at risk free rate = 0.75*(110-100) = $                 7.50

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