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%.

1-What is the price of the put according to the Black-Scholes equation?

2-Under what circumstances does the investor make a profit?

3-Under what circumstances will the option be exercised?

4-Draw a diagram showing the variation of the investor's profit with the stock price at the maturity of the option.

5-Sketch how the value of the option varies with the stock price three months out, one month out, and on maturity