Let S = {S(t) | t 0} be the price process of some stock (e.g., AOL shares). Let C(t) denote the value at time t of a (European) call option written on S with maturity date T and exercise price K. Then C(T) = max[0,S(T)K]. Draw a graph, plotting C(T) versus S(T). This is called the payoff graph for the this call option. The profit graph is the plot of C(T )C(0) versus S(T). Draw the profit graph. For what values of S(T) will the profit be positive ? (This profit ignores the time value of money.)

Question: Leave K as a parameter in your graph and your answer.

Repeat Exercise 2.39 but for the (European) put option. The difference between a put and a call is that with the put you have the right to sell rather than the right to buy. If P(t) is the value of this put with strike price K and expiry date T, explain why P(T) = max[0,KS(T)]. Plot P(T) versus S(T ), and P (T ) P (0) versus S(T ). If you want to take a numerical example, choose the AOL/AUG03/16.00/PUT with P(0) = 0.45USD. For what values of S(T) will the profit be positive? Explain why the holding of a put option on S is like holding an insurance policy over S.

Question: leave K as a parameter in your graph and your answer.