Reference no: EM133056306

1. We will derive a two-state put option value in this problem. Data: S_0= 100; X = 110; 1 + r = 1.10 . The two possibilities for S_T are 130 and 80.

a. Show that the range of S is 50, whereas that of P is 30 across the two states. What is the hedge ratio of the put?

b. Form a portfolio of three shares of stock and five puts. What is the (non-random) payoff to this portfolio? What is the present value of the portfolio?

c. Given that the stock currently is selling at 100, solve for the value of the put.

2. Calculate the value of a call option on the stock in the previous problem with an exercise price of 110. Verify that the put-call parity theorem is satisfied by your answers to this problem and Problem 9. (Do not use continuous compounding to calculate the present value of Xin this example because we are using a two-state model here, not a continuous-time Black-Scholes model.)

3. You are attempting to value a call option with an exercise price of $100 and 1 year to expiration. The under-lying stock pays no dividends, its current price is $100, and you believe it has a 50% chance of increasing to $120 and a 50% chance of decreasing to $80. The risk-free rate of interest is 10%.

Calculate the call option's value using the two-state stock price model.

4. Consider an increase in the volatility of the stock in the previous problem. Suppose that if the stock increases in price, it will increase to $130, and that if it falls, it will fall to $70. Show that the value of the call option is now higher than the value derived in the previous problem.