Suppose some stock currently selling for $80 will either increase in value over the next year to $100, or decrease in value to $64. The risk free rate over the period is 10% given annual compounding. [Let r denote the continuously compounded rate per year. Thus e r×1 = 1.1.] A call option on the stock with an exercise price of $75 matures in one period (1 year).
(a) What are u and d?
(b) What are the payoffs from the call in each state of the world?
(c) What position in the underlying stock and bonds would allow you to replicate the payoff from the call? What is the cost of this replicating portfolio? What is the the call price at time 0?