Question

We will derive a two-state put option value in this problem. Data: S0 = 300; X = 310; 1 + r = 1.1. The two possibilities for ST are 350 and 150. a. The range of S is 200 while that of P is 160 across the two states. What is the hedge ratio of the put? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Hedge ratio b-1. Form a portfolio of 4 shares of stock and 5 puts. What is the (nonrandom) payoff to this portfolio? (Round your answer to 2 decimal places.) Nonrandom payoff $ b-2. What is the present value of the portfolio? (Round your answer to 2 decimal places.) Present value $ c. Given that the stock currently is selling at 300, calculate the put value. (Round your answer to 2 decimal places.) Put value $

Answer 1

We are given : Spot Price (S₀) = 300; Strike Price (X) = 310 ; Interest Rate (r) = 10%; Possible Expiry Prices (S_T) = 350 or 150.

Hedge ratio : change in the price of put option / change in the underlying price (note that the put delta is negative). Hence Hedge ratio = - 160/200 = -0.8

Portfolio : 4 * stock + 5 puts. Let the put price be P. Then the portfolio value today will be :

4 * 300 + 5P = 1200 + 5P

At time T, the portfolio value can be either :

• If S_T = 350; then the portfolio value = 4*350 (puts expire worthless) = 1400
• If S_T = 150; then the portfolio value = 4*150 + 5 * (310-150) = 1400
• Hence the pay off will be same in either case.

Thus the nonrandom pay off will be 1400

PV of the portfolio = 1400/(1+r) = 1400/1.1 = 1272.73

Since the current value of the portfolio should equal the PV of the expected payoff at time T (for their to be no arbitrage):

1200 + 5P = 1272.73 or P = 14.55 (put value)