Suppose that, in each period of a two-period stock price model, the cost of a security either goes up by a factor of u = 2 or down by a factor d = 1/2. Assume the initial price of the security is $80 and that the interest rate r is 0.

a). Compute the risk neutral probabilities p (price moves up) and q = 1 p (price moves down) for this model.

b). Sketch a diagram of this two period stock price model.

c). Assuming the strike price of a European call option on this security is $70, compute the possible payos of the call option given that the option expires in two periods.

d). What is the expected value of the payo of the call option?

e). What should the no-arbitrage price of the call option be?