Question 2 (15 points) Consider a two-period (t = 0,1) market with two assets: a risk free bond with face value $1 and rate of return r = 0.1; and a stock, whose current price is go. The future price q is uncertain, and it can take one of the two values q = {qh, q}, where qh > qo(1+r) > q. (a) Suppose that h = $120 and q = $90. An investor uses the past stock price dynamics to estimate that the probabilities of the stock price qi taking either of the values are 50:50. Therefore, she evaluates the current stock price as 90 0.5gh + 0.5g 110 1+r $95.44. 1.1 The investor observes that the current price of the stock, is not $95.44, but $98.18, and decides that the stock is overpriced by the market. Is the investor right? Explain why or why not. (b) There is also the European call option on the stock with the strike $100 and maturity date at t = 1. What is the payoff on the option at t = 1? Create a replicating portfolio for the call and calculate the option price at t = 0. (c) Show that if the option price is different from the value you found in (b), then it is possible to create an arbitrage portfolio. (d) Consider the American put option on the stock with the maturity date t = 1 and the strike 90 < K < 120. For which values of K the option will be exercised prematurely?