Suppose that spot gold is at 350. Suppose the volatility of the return on gold is 15%, and the 90- day risk free rate is 4% per year.

a. Compute the price of an at-the-money European call option and an at-the-money European put option with 90 days to expiration. Also, compute the respective hedge ratios. Use the Black-Scholes model but do not use a computer program. Show all your computations.

b. Repeat a) for the strike prices of 330, 340, 360 and 370. Plot the relationship between the option price and gold prices. Plot the relationship between the hedge ratio and gold prices? You can use a programmed Black-Scholes model.

c. For volatilities of 10%, 15%, 20%, 25%, and 30%, plot the relationship between the option price and gold prices. Plot the relationship between the hedge ratio and gold prices.

d. For time to expiration of 30 days, 60 days, 90 days, 120 days, and 150 days, plot the relationship between the option price and gold prices. Plot the relationship between the hedge ratio and gold prices.

e. For risk free rates of 2%, 4%, 6%, 8%, and 10%, plot the relationship between the option price and gold prices. Plot the relationship between the hedge ratio and gold prices.