Consider a non-dividend-paying stock. The current stock price is $100, its volatility is 20%, and the risk-free interest rate is 1%.

(a) Using Black-Scholes-Merton, what is the price of a 5-year European call option on the stock, with a strike price of $99?

(b) Suppose the volatility of the stock increases to 40%. What is the price of the option now? (c) Suppose instead that the volatility of the stock goes to 1%. What would you be willing to pay for the option? Compare to your answer in b, and explain why they are different.