12. Consider a derivative that pays off 3&1 at time T. where ST is the stock price at that time. When the stock price follows geometric Brownian motion, it can be shown that its price at time t (t a; T) has the form an, 1'\"an where S is the stock price at time t and h. is a function only off and T. a. By substituting into the BlackScholes partial differential equation, derive an ordinary dif ferential equation satised by hlt, T}. b. What is the boundary condition for the differential equation for Mt, T} ? c. Show that h. T) = g['3'5'32\"{Tllil+vl:n1]{T_1] where r is the riskfree interest rate and or is the stock price volatility