For the following three problems, assume dSt = constants. Letr be the constant interest rate. aSidt + SidW, where a ER,O > 0 are Problem 4 (10 points). Recall that the payoff of a European put option with strike K at terminal time T is (K - ST)+. It is easy to observe that ST - K = (ST - K)+ - (K - ST)+. Based on this observation and the Black-Schoes formula, deduce a formula for the price of this put option at time t = 0. Support with reasoning (such as indicating which formula/theorem you are using); a final answer alone will lose at least half credit. For the following three problems, assume dSt = constants. Letr be the constant interest rate. aSidt + SidW, where a ER,O > 0 are Problem 4 (10 points). Recall that the payoff of a European put option with strike K at terminal time T is (K - ST)+. It is easy to observe that ST - K = (ST - K)+ - (K - ST)+. Based on this observation and the Black-Schoes formula, deduce a formula for the price of this put option at time t = 0. Support with reasoning (such as indicating which formula/theorem you are using); a final answer alone will lose at least half credit