8. (20 points) Black-Scholes Formula and Probability of Exercise Letr be the risk free rate. Let S be the current price of a stock with annualized volatility o and continuously compounded dividend yield 8. Let C(S,K,0,1,5,8) be the price of a European-style call option on the stock with strike price K and time to expiration T in years. a) State the Black-Scholes formula for C(S, K, 0,6,7,8). Provide the main formula and formulas for dy and d2. b) Use put-call parity and your result in a) to derive the main formula for P(S,K, 0,6,7,8). 8. (20 points) Black-Scholes Formula and Probability of Exercise (continued) c) Suppose that in ST ~N (In S+(r-8-502)T, 0T). Demonstrate that P(St > K) = N(D2). d) Write C(S, K, 0,1, 7, 8) as the discounted expected value of the value of call exercise at time T. Demonstrate how this formula confirms the strike term in the Black-Scholes formula for C(S,K, 0,r, T,8)