Problem 8. Simple application of Black-Scholes formula (7 pts) In this question, we consider a Black-Scholes model with a risk-free asset and a stock. (a) (2 pts) Assume that the stock price is $51, the interest rate is %11 compounded continuously, 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) (2.5 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) (2.5 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 8. Simple application of Black-Scholes formula (7 pts) In this question, we consider a Black-Scholes model with a risk-free asset and a stock. (a) (2 pts) Assume that the stock price is $51, the interest rate is %11 compounded continuously, 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) (2.5 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) (2.5 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%