At time zero the price of a non-dividend-paying stock is So. Suppose that the time interval between 0 and T is divided into two subintervals of length t\ and t2. During the first subinterval, the risk-free interest rate and volatility are r, and ax, respectively. During the second subinterval, they are r2 and a2, respectively. Assume that the world is risk neutral.

a. Use the results in Chapter 11 to determine the stock price distribution at time T in terms of r\, r2, <7i, a2, t\, t%, and SQ.

b. Suppose that r is the average interest rate between time zero and T and that V is the average variance rate between times zero and T. What is the stock price distribution as a function of T in terms of r, V, T, and 50?

c. What are the results corresponding to

(a) and

(b) when there are three subintervals with different interest rates and volatilities?

d. Show that if the risk-free rate, r, and the volatility,