Suppose that the current price of a stock is $120 per share with volatility σ = 50% per annum. Suppose further that the risk-free interest rate is 7% per annum and the stock pays no dividend.
(a) What is the price of a European call option contingent on the stock with a strike price of $125 that will expire in 3 months?
(b) What is the price of a European put option on the same stock with a strike price of $118 that will expire in 3 months? If the volatility σ is increased to 80% per annum, then what are the prices of the two options?