(Intrinsic value vs. Black–Scholes value) Consider the data below.

a. Produce a graph comparing a call’s intrinsic value (defined as Max(S – X, 0)) and its Black–Scholes price for S = 20, 25, . . ., 70.
From this graph you should be able to deduce that it is never optimal to exercise early a call priced by the Black–Scholes.

b. Produce the same graph comparing a put’s intrinsic value (= Max(X – S, 0)) and its Black–Scholes price. From this graph you should be able to deduce that it is may be optimal to exercise early a put priced by the Black–Scholes formula.

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A B 2 S 3 X 4 T 5r 6 Sigma 50 Current stock price 50 Exercise price 0.50 Time to maturity of option (in years) 4.00% Risk-free rate of interest 35% Stock volatility