Problem 3. (10 points) In this question, we consider a Black-Scholes model with a risk-free asset and a stock. (a) (3 pts) Assume that the stock price is $51, the interest rate is 11% compounded con- tinuously, and the stock volatility is 25%. What is the price of a European call option on the stock with the strike price $49 and maturity of 3 months? (b) (4 pts) Assume the same setting as in part (a). Find the zero-valued delta-neutral portfolio, taking positions (x,y,1) in the stock, the risk-free asset, and the European call option. (c) (3 pts) What is the price of a European put option on the stock, with the strike price $69 and maturity of 6 months, when the stock price is $68, the interest rate is 5% compounded continuously, and the stock volatility is 30%? Problem 3. (10 points) In this question, we consider a Black-Scholes model with a risk-free asset and a stock. (a) (3 pts) Assume that the stock price is $51, the interest rate is 11% compounded con- tinuously, and the stock volatility is 25%. What is the price of a European call option on the stock with the strike price $49 and maturity of 3 months? (b) (4 pts) Assume the same setting as in part (a). Find the zero-valued delta-neutral portfolio, taking positions (x,y,1) in the stock, the risk-free asset, and the European call option. (c) (3 pts) What is the price of a European put option on the stock, with the strike price $69 and maturity of 6 months, when the stock price is $68, the interest rate is 5% compounded continuously, and the stock volatility is 30%