3. One-Step Binomial Model

Consider a 2-year European call with strike price $100. The current stock price is $100 and the stock price can move either up or down by 30% once during the life of the option (that is, u= 1.3 and d= 0.7). The risk-free interest rate is 4% per annum.

(a) Find the option payoff at each of two stock prices at the expiration.

(b) Suppose that we are in time 0. Find the replicating portfolio of the option.

(c) What is the current price of the option?

(d) What is the realized return on call when the stock price moves up? What is the realized return on call when the stock price moves down? (Hint: Find the realized gross return on the call. If the stock price moves up, the return is fu/f0.)

4. Option Pricing in Discounted Cash Flow

Lets revisit the European call in Question 3. This time, we want to use the DCF approach to determine the option price. Risk-averse investors require the return on stock to be 10% per annum.

(a) What is the real probability p of an increase in the stock price?

(b) What is the discount rate for the call option in DCF? Find the annual rate rcall in continuous compounding.

(c) What is the current price of the call from DCF? Is this price the same as the price from Question 3 (c)?