Sample Option Problems

Question 1

Calculate the call premium predicted by the Black and Scholes model for a non-dividend paying stock that has a volatility of 40% a market price of \$33.50 an exercise price of \$35 and one month remaining until expiration. Use a risk-free rate of 5%. Calculate the present value of the exercise with continuous compounding.

Question 2

Calculate the call premium predicted by the Black and Scholes model for a non-dividend paying stock that has a volatility of 35% a market price of \$108.50 an exercise price of \$110 and 15 days remaining until expiration. Use a risk-free rate of 4%. Calculate the present value of the exercise with continuous compounding.

Question 3

Calculate the put premium predicted by the Black and Scholes model for a non-dividend paying stock that has a volatility of 30% a market price of \$66 an exercise price of \$65 and three months remaining until expiration. Use a risk free rate of 3%. Use the put-call parity relationship to adjust from a call premium. Calculate the present value of the exercise with continuous compounding.

Question 4

Use the Black and Scholes model to estimate how many shares you would want to put into the tracking portfolio for a call on the stock under the following conditions. Price of the stock is \$51.00. Present value of the exercise price of the call option is \$49.00. The risk free interest rate is 5%. The stock's standard deviation is 20%. The call option matures in three months.

Question 5

Given a call option with a premium of \$3, an exercise price of \$35 on a common stock that presently sells in the market for \$38. The available risk-free rate is 5%. Show how you can earn an arbitrage profit.