Problem 1 (20 marks)

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

S₀ = $20, X =$20, r =5% (c.c.), T = 0.5 year, s = 0.20

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.

Answer the following questions:

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 $16, $18, $20, $22, or $24?