The payoff function of a contract at maturity T is given below, C(ST?,T)={lnKST??,ST?>K0,ST??K? where K is the strike price and St? is the current price of a risky stock. The stoc does not pay dividends. K is a constant parameter. In the Black-Scholes framework, price this contract by partial differential equation approach. You need to show clear derivation steps.

(30 points) The payoff function of a contract at maturity T is given below, C(S,, T) = In , S, > K K 0, S,SK where K is the strike price and S, is the current price of a risky stock. The stock does not pay dividends. K is a constant parameter. In the Black-Scholes framework, price this contract by partial differential equation approach. You need to show clear derivation steps.(30 points) The payoff function of a contract at maturity T is given below, C(S,, T) = In , S, > K K 0, S,SK where K is the strike price and S, is the current price of a risky stock. The stock does not pay dividends. K is a constant parameter. In the Black-Scholes framework, price this contract by partial differential equation approach. You need to show clear derivation steps