An Introduction to Derivatives and Risk Management 10th Edition By Don M. - Test Bank

An Introduction to Derivatives and Risk Management 10th Edition By Don M. – Test Bank

 

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Sample Questions Are Posted Below

 

CHAPTER 5: OPTION PRICING MODELS: THE BLACK-SCHOLES-MERTON MODEL

 

 

MULTIPLE CHOICE TEST QUESTIONS

 

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

 

No dividends are expected.

 

Use this information to answer questions 1 through 8.

 

1. 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.)
2. 5.35
3. 1.10
4. 4.73
5. 6.50
6. none of the above

 

2. Suppose you feel that the call is overpriced. What strategy should you use to exploit the apparent mis-valuation? (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 shares.)
3. buy 791 shares, sell 1,000 calls
4. buy 705 shares, sell 1,000 calls
5. sell short 791 shares, buy 1,000 calls
6. sell short 705 shares, buy 1,000 calls
7. none of the above

 

3. The price of a put on the stock is: (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.)
4. 0.85
5. 8.64
6. 2.35
7. 4.88
8. none of the above

 

4. To construct a riskless hedge, the number of puts per 100 shares purchased is: (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 0.01.)
5. 0.7580
6. 0.2420
7. –0.2480
8. –0.6628
9. none of the above

 

5. The call’s vega is: (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 0.05.)
6. –3.02
7. 0.046
8. –0.792
9. 4.67
10. none of the above

 

6. If the actual call price is 3.79, the implied standard deviation is
7. 0.25
8. greater than 0.25
9. less than 0.25
10. infinite
11. none of the above

 

7. 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.)
8. 22.60
9. 19.65
10. 23.00
11. 21.99
12. none of the above

 

8. If we now assume that the stock pays a single dividend of 2.25 in three months, 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.)
9. 17.75
10. 20.75
11. 20.00
12. 20.80
13. none of the above

 

9. If the simple return on a Treasury bill is 8.5 percent, the risk-free rate in the Black-Scholes-Merton model is
10. 8.77 percent
11. 8.93 percent
12. 8.55 percent
13. 8.20 percent
14. none of the above

 

10. Which of the following variables in the Black-Scholes-Merton option pricing model is the most difficult to obtain?
11. the volatility
12. the risk-free rate
13. the stock price
14. the time to expiration
15. the exercise price

 

11. The binomial price will theoretically equal the Black-Scholes-Merton price under which of the following conditions?
12. when the number of time periods is large
13. when the option is at-the-money
14. when the option is in-the-money
15. when the option is out-of-the-money
16. none of the above

 

12. If the stock price is 44, the exercise price is 40, the put price is 1.54, and the Black-Scholes-Merton price using 0.28 as the volatility is 1.11, the implied volatility will be
13. higher than 0.28
14. lower than 0.28
15. 0.28
16. lower than the risk-free rate
17. none of the above

 

13. Which of the following statements about the Black-Scholes-Merton model is not true?
14. decreasing the volatility lowers the call price
15. the expected stock price plays a role in the model
16. the risk-free rate is continuously compounded
17. the model is consistent with put-call parity
18. none of the above

 

14. Which of the following characteristics of the Black-Scholes-Merton model is not correct?
15. it is a discrete time model
16. it is the limit of the binomial model
17. it is a continuous time model
18. it gives the price of a European option
19. none of the above

 

15. Which of the following assumptions of the Black-Scholes-Merton model is not correct?
16. the stock volatility is constant
17. the stock return follows a normal distribution
18. there are no transaction costs
19. there are no taxes
20. none of the above

 

16. Which of the following statements about the delta is not true?
17. it ranges from zero to one
18. it converges to zero or one at expiration
19. it is given by N(d₁) in the Black-Scholes-Merton model
20. it changes slowly near expiration if the option is at-the-money
21. none of the above

 

17. Which of the following “Greeks” is not a measure of the option’s sensitivity to a change in one of its input values?
18. delta
19. gamma
20. rho
21. theta
22. sigma

 

18. Which of the following statements is true about the relationship between the option price and the risk-free rate?
19. a call price is nearly linear with respect to the risk-free rate
20. a call price is highly sensitive to the risk-free rate
21. the risk-free rate affects a call but not a put
22. the risk-free rate does not affect a call price
23. none of the above

 

19. The relationship between the volatility and the time to expiration is called the
20. volatility smile
21. volatility skew
22. term structure of volatility
23. theta
24. none of the above

 

20. What is the reason for executing a gamma hedge?
21. the volatility can change
22. the stock price can make a large move
23. the stock price moves are too small for a delta hedge to work
24. there is no true risk-free rate
25. none of the above

 

21. Which of the following statements about the volatility is not true?
22. the implied volatility often differs across options with different exercise prices
23. the implied volatility equals the historical volatility if the option is correctly priced
24. the implied volatility is determined by trial and error
25. the implied volatility is nearly linearly related to the option price
26. none of the above

 

22. The relationship between the option price and the exercise price is called
23. the gamma
24. the vega
25. the omega
26. the zeta
27. none of the above

 

23. What happens when the volatility is zero in the Black-Scholes-Merton model?
24. the option price converges to either zero or the lower bound
25. the option price converges to the intrinsic value
26. the option automatically expires out of the money
27. the gamma and delta converge
28. none of the above

 

24. Which of the following is not correct about a call’s gamma?
25. it is the same as a put’s gamma
26. it is large when the call is at-the-money
27. it can be viewed as a measure of the risk of the delta
28. it is a source of risk that can be hedged only by using another option
29. none of the above

 

25. Which of the following statements is incorrect about the historical volatility?
26. if used in the Black-Scholes-Merton model, it gives the current market price
27. it is based on the volatility of the log return on the stock
28. it requires a sample of recent returns
29. it should be converted to an annualized volatility
30. none of the above

 

26. A hedge portfolio is established and maintained by constantly adjusting the relative proportions of stock and options, a process referred to as
27. actively managing
28. continuous reconciliation
29. marking to market
30. dynamic trading
31. none of the above

 

27. The standard normal random variable used in the calculation of cumulative normal probabilities within the Black-Scholes-Merton option pricing model is
28. the lognormal distribution
29. the d₁ and d₂ statistic
30. the z statistic
31. the f distribution
32. none of the above

 

28. The pattern of volatility across exercise prices is often called
29. the price-fluctuation graph
30. the volatility smile
31. the term structure of implied volatility
32. the skew
33. none of the above

 

29. The Black-Scholes-Merton model for European puts, obtained by applying put-call parity to the Black-Scholes-Merton model for European calls, is customarily expressed by which of the following:
34. none of the above

 

30. The implied volatility is obtained by finding the standard deviation that, when used in the Black-Scholes-Merton model, makes the
31. model price expire at zero
32. model price equal the market price of the option
33. model price such that it exceeds currently traded market option values
34. model price equal the intrinsic value of the underlying stock
35. none of the above

 

CHAPTER 5: OPTION PRICING MODELS: THE BLACK-SCHOLES-MERTON MODEL

 

TRUE/FALSE TEST QUESTIONS

 

T             F               1.           The Black-Scholes-Merton model is the discrete time limit to the binomial model.

 

T             F               2.           In the Black-Scholes-Merton model, stock prices are assumed to behave randomly.

 

T             F               3.           The values of N(d₁) and N(d₂) are called risk neutral probabilities.

 

T             F               4.           An option’s gamma represents the risk of the delta changing.

 

T             F               5.           The binomial model always gives the same option price as the Black-Scholes-Merton model.

 

T             F               6.           The Black-Scholes-Merton model assumes that the volatility does not change throughout the option’s life.

 

T             F               7.           One of the variables that influences the price of the option is the expected return on the stock.

 

T             F               8.           The option’s rate of time value decay is represented by its theta.

 

T             F               9.           The option’s delta is approximately the change in the option price for a change in the stock price.

 

T             F             10.           Since dividends could trigger an early exercise of an American call, the Black-Scholes-Merton dividend adjustment will provide the correct price of an American call.

 

T             F             11.           The Black-Scholes-Merton option price is relatively insensitive to changes in the risk-free rate.

 

T             F             12.           One of the inputs to the Black-Scholes-Merton model is the volatility over a recent time period.

 

T             F             13.           When the risk–free rate is zero, the Black–Scholes formula converges to the intrinsic value.

 

T             F             14.           In order to compute the implied volatility, one must force the option to be correctly priced by the model.

 

T             F             15.           The Black-Scholes-Merton model combined with put-call parity give the theoretical price of an American put option.

 

T             F             16.           Vega captures the combined effects of time decay and volatility.

 

T             F             17.           The volatility smile is the relationship between implied volatility and historical volatility.

 

T             F             18.           The Black-Scholes-Merton formula requires cumulative probabilities from the lognormal distribution.

 

T             F             19.           In the term structure of volatility, the forward volatility is the expected future volatility.

 

T             F             20.           A riskless hedge requires more shares of stock than call options.

 

T             F             21.           An approximate implied volatility for an at-the-money call can be solved directly.

 

T             F             22.           The implied volatilities of a call and a put with the same terms should be the same.

 

T             F             23.           The historical volatility is the same value as the implied volatility.

 

T             F             24.           The option’s sensitivity to an interest rate change is called rho.

 

T             F             25.           The time to expiration of an option is based on a 360-day year.

 

T             F             26.           The Black-Scholes-Merton model can be used with currency options by replacing the dividend yield with the foreign interest rate.

 

T             F             27.           The Black-Scholes-Merton model is the best model for valuing all types of options.

 

T             F             28.           The Black-Scholes-Merton model assumes the underlying instrument movement is lognormally distributed.

 

T             F             29.           The Black-Scholes-Merton model assumes that the underlying company never goes bankrupt.

 

T             F             30.           The level of liquidity of the underlying instrument will influence the behavior of related options.