Assume the Black-Scholes framework. Let S(t) denote the time-t price of a stock. You are given The current time is t. The stocks volatility is o per annum. The dividend yield of the stock is & per year. The continuously compounded expected return on the stock is a per an- num. The continuously compounded risk-free interest rate is r per annum. Let P(t) denote the time-t price of a K-strike (T t)-year European put option of the stock. For a given r, a, T, 8 and o, (a) derive the conditional expectation of S(T) given that the put option ex- pires out-of-the money. The final expression of your answer should in term of the cumulative distribution function of standard normal distribution. (SHOW all the working steps clearly). Assume the Black-Scholes framework. Let S(t) denote the time-t price of a stock. You are given The current time is t. The stocks volatility is o per annum. The dividend yield of the stock is & per year. The continuously compounded expected return on the stock is a per an- num. The continuously compounded risk-free interest rate is r per annum. Let P(t) denote the time-t price of a K-strike (T t)-year European put option of the stock. For a given r, a, T, 8 and o, (a) derive the conditional expectation of S(T) given that the put option ex- pires out-of-the money. The final expression of your answer should in term of the cumulative distribution function of standard normal distribution. (SHOW all the working steps clearly)