Assume that a non-dividend-paying stock has an expected return of a and a volatility of o. An innovative financial institution has just announced that it will trade a security that pays off a dollar amount equal to In Sr at time 7, where Sy denotes the value of the stock price at line 7.

(a) Use risk-neutral valuation to calculate the price of the security at time in terms of the stock price, 8, at time.

(b) Confirm that your price satisfies the differential equation (13.16)