Derivatives

14. The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European put option on the stock with a strike price of $32 that expires in 6 months with u = 1.1 and d = 0.9. Each step is 3 months, the risk free rate is 8%. A. $2.24 B. $2.44 C. $2.64 D. $2.84

A

3. An investor has exchange-traded put options to sell 100 shares for $20. There is a $1 cash dividend. Which of the following is then the position of the investor? A. The investor has put options to sell 100 shares for $20 B. The investor has put options to sell 100 shares for $19 C. The investor has put options to sell 105 shares for $19 D. The investor has put options to sell 105 shares for $19.05

A

10. The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells six-month call options with a strike price of $32. Which of the following hedges the position? A. Buy 0.6 shares for each call option sold B. Buy 0.4 shares for each call option sold C. Short 0.6 shares for each call option sold D. Short 0.4 shares for each call option sold

B

13. The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 8% per annum with continuous compounding. What is the option price when u = 1.1 and d = 0.9? A. $1.29 B. $1.49 C. $1.69 D. $1.89

B

16. If the volatility of a non-dividend-paying stock is 20% per annum and a risk-free rate is 5% per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter p for a tree with a three-month time step? A. 0.50 B. 0.54 C. 0.58 D. 0.62

B

17. The current price of a non-dividend paying stock is $50. Use a two-step tree to value an American put option on the stock with a strike price of $48 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum, and the volatility is 20%. Which of the following is the option price? A. $1.95 B. $2.00 C. $2.05 D. $2.10

B

6. The price of a stock, which pays no dividends, is $30 and the strike price of a one year European call option on the stock is $25. The risk-free rate is 4% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? A. $5.00 B. $5.98 C. $4.98 D. $3.98

B

1. An investor has exchange-traded put options to sell 100 shares for $20. There is a 2 for 1 stock split. Which of the following is the position of the investor after the stock split? A. Put options to sell 100 shares for $20 B. Put options to sell 100 shares for $10 C. Put options to sell 200 shares for $10 D. Put options to sell 200 shares for $20

C

11. The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. What is the risk-neutral probability of that the stock price will be $36? A. 0.6 B. 0.5 C. 0.4 D. 0.3

C

4. The price of a stock is $67. A trader sells 5 put option contracts on the stock with a strike price of $70 when the option price is $4. The options are exercised when the stock price is $69. What is the trader's net profit or loss? A. Loss of $1,500 B. Loss of $500 C. Gain of $1,500 D. Loss of $1,000

C

9. The price of a European call option on a stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. A dividend of $1 is expected in six months. What is the price of a one-year European put option on the stock with a strike price of $50? A. $8.97 B. $6.97 C. $3.06 D. $1.12

C

12. The current price of a non-dividend-paying stock is $40. Over the next year it is expected to rise to $42 or fall to $37. An investor buys put options with a strike price of $41. What is the value of each option? The risk-free interest rate is 2% per annum with continuous compounding. A. $3.93 B. $2.93 C. $1.93 D. $0.93

D

15. If the volatility of a non-dividend paying stock is 20% per annum and a risk-free rate is 5% per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter u for a tree with a three-month time step? A. 1.05 B. 1.07 C. 1.09 D. 1.11

D

2. An investor has exchange-traded put options to sell 100 shares for $20. There is 25% stock dividend. Which of the following is the position of the investor after the stock dividend? A. Put options to sell 100 shares for $20 B. Put options to sell 75 shares for $25 C. Put options to sell 125 shares for $15 D. Put options to sell 125 shares for $16

D

5. The price of a stock is $64. A trader buys 1 put option contract on the stock with a strike price of $60 when the option price is $10. When does the trader make a profit? A. When the stock price is below $60 B. When the stock price is below $64 C. When the stock price is below $54 D. When the stock price is below $50

D

7. A stock price (which pays no dividends) is $50 and the strike price of a two year European put option is $54. The risk-free rate is 3% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? A. $4.00 B. $3.86 C. $2.86 D. $0.86

D

8. The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. What is the price of a one-year European put option on the stock with a strike price of $50? A. $9.91 B. $7.00 C. $6.00 D. $2.09

D