Question 1  A stock priced at 60 can go up or down by 10% per period. The risk-free rate is 4% per period. Which of the following is the correct price of an American put with an exercise price of 58 when using a two binomial model?

 a. 6.79

 b.  3.52

 c. 5.05

 d. 1.79

  e. 6.21

Question 2 The following information is given about options on the stock of a certain company.

S₀ = 28                   X = 20

r_c = 0.15                T = 0.5

s² = 0.25

3. If we now assume that the stock pays a single dividend of 2.75 in 150 days, what stock price should we use in the model? (Due to differences in rounding your calculations may be slightly different. "none of the above" should be selected only if your answer is different by more than 10 cents.)

       a. 25.25
       b. 25.38
       c. 25.00
       d. 30.75
       e. none of the above

4. What is the profit on a bull money spread using the June 45/50 calls if the stock price at expiration is $51?

       a. -102
       b. $398
       c. $417
       d. -241
       e. none of the above

5. The following prices are available for call and put options on a stock priced at $50.  The risk-free rate is 6 percent and the volatility is 0.35.  The March options have 90 days remaining and the June options have 180 days remaining.  The Black-Scholes model was used to obtain the prices.

Question 6. A futures contract covers 5000 pounds with a minimum price change of $0.01 is sold for $32.60 per pound. If the initial margin is $2,750 and the maintenance margin is $2,000, at what price would there be a margin call?

      a. 31.91
      b. 32.75
      c. 32.11
      d. 31.29
      e. 31.80

7. On March 2, a Treasury bill expiring on April 20 had a bid discount of 5.80, and an ask discount of 5.86.  What is the best estimate of the risk-free rate as given in the text?

8. The stock price was 113.25.  The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January).  The times to expiration were 0.0384 (November), 0.1342 (December), and 0.211 (January).  Assume no dividends unless indicated.

9. Consider a binomial world in which the current stock price of 80 can either go up by 10 percent or down by 8 percent.  The risk-free rate is 4 percent.  Assume a one-period world.  Answer questions 12 through 15 about a call with an exercise price of 80.

10. What is the theoretical value of the call?

11.. A stock priced at 50 can go up or down by 10 percent over two periods.  The risk-free rate is 4 percent.  Which of the following is the correct price of an American put with an exercise price of 55?

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

S₀ = 23                   X = 20

r_c = 0.09                                T = 0.5

s² = 0.15

13. What value does the Black-Scholes-Merton model predict for the call? (Due to differences in rounding your calculations may be slightly different. "none of the above" should be selected only if your answer is different by more than 10 cents.)

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

S₀ = 23                   X = 20

r_c = 0.09                                T = 0.5

s² = 0.15

15. If we now assume that the stock pays a dividend at a known constant rate of 3.5 percent, what stock price should we use in the model? (Due to differences in rounding your calculations may be slightly different. "none of the above" should be selected only if your answer is different by more than 10 cents.)

16. Consider a stock priced at $30 with a standard deviation of 0.3.  The risk-free rate is 0.05.  There are put and call options available at exercise prices of 30 and a time to expiration of six months.  The calls are priced at $2.89 and the puts cost $2.15.  There are no dividends on the stock and the options are European.  Assume that all transactions consist of 100 shares or one contract (100 options). 

17. What is the breakeven stock price at expiration $27?

18. The following prices are available for call and put options on a stock priced at $50.  The risk-free rate is 6 percent and the volatility is 0.35.  The March options have 90 days remaining and the June options have 180 days remaining.  The Black-Scholes model was used to obtain the prices.

19. A futures contract covers 5000 pounds with a minimum price change of $0.01 is sold for $31.60 per pound. If the initial margin is $2,525 and the maintenance margin is $1,000, at what price would there be a margin call?