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,K−S(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.