4. Assume that a non-dividend paying stock has an expected return of and volatility of . A financial institution launches a security that pays off a dollar amount of ln ST at time T, where ST denotes the value of the stock price at time T.

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

(b) Confirm that your price satisfies the Black-Scholes-Merton differential equation.