A financial institution plans to offer a security that pays off a dollar amount equal to S at time T, where Sy is the price at time 7 of a stock that pays no dividends.

(a) Use risk-neutral valuation to calculate the price of the security at time t in terms of the stock price S at time t. (Hint: The expected value of S can be calculated from the mean and variance of Sr given in Section 14.1.)

(b) Confirm that your price satisfies the differential equation (14.16).