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

S: 50

X: 50

T: .5

r: 4%

sigma: 35%

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.

C. The call option is always greater than its immediate exercise value (s-x) for s > x. Use the put option procing model to find such an example

8. (Intrinsic value vs. Black-Scholes value) Consider the data below. a. Produce a graph comparing a call's intrinsic value (defined as Max(SX,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(XS,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