(1 pt) This problem finds the formula for a cash-or-nothing Put option as the solution W(S,t) of the Black-Scholes equation with payoff at Tgiven by the function A(S) = 1for0 K Here K is a positive constant. The method is by expressing W(S, t) in terms of a related solution of the heat equation (2)?? Assume the substitutions In(S)(r-T-t) allow expressing the solution W(S, of (1), as (5) W"( S, t)-e-r(T-t)u(z, ?) where u , T satisfies (2). Then t = T corresponds to T (8) u(z, 0) = | Assume the solution u(,T) of the heat equation (2) for this initial data is and the initial data u(, 0 must be for r K Here K is a positive constant. The method is by expressing W(S, t) in terms of a related solution of the heat equation (2)?? Assume the substitutions In(S)(r-T-t) allow expressing the solution W(S, of (1), as (5) W"( S, t)-e-r(T-t)u(z, ?) where u , T satisfies (2). Then t = T corresponds to T (8) u(z, 0) = | Assume the solution u(,T) of the heat equation (2) for this initial data is and the initial data u(, 0 must be for r