Problem 1. An investor buys a European style put option. The stock price is $42 and the strike price is $40. The option has ninety days until maturity. The risk-free rate stands at 1.6%, and the volatility of the stock returns is 49%. a) What is the price of the put according to the Black-Scholes equation? b) Under what circumstances does the investor make a profit? c) Under what circumstances will the option be exercised? d) Draw a diagram showing the variation of the investor's profit with the stock price at the maturity of the option. e) Sketch how the value of the option varies with the stock price three months out, one month out, and on maturity