Problem 1 (25 points)

The following information is given about options on the stock of a certain company:

S₀ = $80, X =$70, r =10% per year (continuously compounded), T = 9 months, = 0.30

No dividends are expected. One option contract is for 100 shares of the stock. All notations are used in the same way as in the Black-Scholes-Merton Model.

1.What is the European call option price and European put option price, according to the Black-Scholes model?

2.What is the cost of buying a protective put?

3.What is the cost of writing a covered call?

4.What will be the payoff and profit of the protective put if the stock price on maturity is $60, $70, $76, $80, $86?

5.What will be the payoff and profit of the covered call if the stock price on maturity is $60, $70, $76, $80, $86?