We will derive a twostate put option value in this problem D

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

a. The range of S is 50 while that of P is 30 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 3 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 200, calculate the put value. (Round your answer to 2 decimal places.)

Put value            $

Solution

a) Hedge Ratio = (Price Up - Price down) /( STrike Price Upper - Strike Price down ) = ( 0-30)/( 230-180) = -3/5 0r -0.6

b) Riskless portfolio =Buy 3 shares+ 5 put s = 3 shares * Strike price down + 5 shares * Put price down= 3 * 180 + 5* 30 = 690
Riskless portfolio =Buy 3 shares+ 5 put s = 3 shares * Strike price up + 5 shares * Put price up= 3 * 230 + 5* 0 = 690

Present Value = 690/1.1 = 627.27

c) Portfolio cost = 3* shares + 5 * puts = 690/1.1
3* 200 + 5* Put Value = 690/1.1
Put value = 5.45
Best of Luck. God Bless