Let p(S, T, X) denote the value of a European put on a stock selling at S dollars, with time to maturity T, and with exercise price X, and let P(S, T, X) be the value of an American put.

a. Evaluate p(0, T, X).

b. Evaluate P(0, T, X).

c. Evaluate p(S, T, 0).

d. Evaluate P(S, T, 0).

e. What does your answer to part

(b) tell you about the possibility that American puts may be exercised early?