Detailed explanation for a-c:

In this question, we consider a Black-Scholes model with a risk-free asset and a stock S. (a) (4 points) Assume that the stock price is S(0= $51, the interest rate is r = 11% compounded continuously, and the stock volatility is o = 25%. What is the price of a European call option on the stock with the strike price X = $49 and maturity of 3 months? (b) (2 points) Assume the same setting as in part (a). Find the zero-valued delt a-neutral portfolio, taking positions (r, y, 1) in the stock, the risk-free asset, and the European call option. (c) (5 Points) What stock price on day 1 makes the delta-neutral portfolio in part (b) attain its maximum value? (d) (4 points) What is the price of a European put option on the stock, with the strike price X = $69 and maturity of 6 months, when the stock price is S(0) = $68, the interest rate is r = 5% compounded continuously, and the stock volatility is o = 30%? In this question, we consider a Black-Scholes model with a risk-free asset and a stock S. (a) (4 points) Assume that the stock price is S(0= $51, the interest rate is r = 11% compounded continuously, and the stock volatility is o = 25%. What is the price of a European call option on the stock with the strike price X = $49 and maturity of 3 months? (b) (2 points) Assume the same setting as in part (a). Find the zero-valued delt a-neutral portfolio, taking positions (r, y, 1) in the stock, the risk-free asset, and the European call option. (c) (5 Points) What stock price on day 1 makes the delta-neutral portfolio in part (b) attain its maximum value? (d) (4 points) What is the price of a European put option on the stock, with the strike price X = $69 and maturity of 6 months, when the stock price is S(0) = $68, the interest rate is r = 5% compounded continuously, and the stock volatility is o = 30%