Hull: Fundamentals of Futures and Options Markets, Ninth Edition
Chapter 13: Valuing Stock Options: The BSM Model
Multiple Choice Test Bank
1. Which of the following is assumed by the Black-Scholes-Merton model?
A. The return from the stock in a short period of time is lognormal
B. The stock price at a future time is lognormal
C. The stock price at a future time is normal
D. None of the above
2. The original Black-Scholes and Merton papers on stock option pricing were published in which
year?
A. 1983
B. 1984
C. 1974
D. 1973
3. Which of the following is a definition of volatility
A. The standard deviation of the return, measured with continuous compounding, in one
year
B. The variance of the return, measured with continuous compounding, in one year
C. The standard deviation of the stock price in one year
D. The variance of the stock price in one year
4. A stock price is $100. Volatility is estimated to be 20% per year. What is an estimate of the
standard deviation of the change in the stock price in one week?
A. $0.38
B. $2.77
C. $3.02
D. $0.76
5. What does N(x) denote?
A. The area under a normal distribution from zero to x
B. The area under a normal distribution up to x
C. The area under a normal distribution beyond x
D. The area under the normal distribution between –x and x
6. Which of the following is true when there are dividends
A. It is never optimal to exercise a call option on the stock early
B. It can be optimal to exercise a call option at any time
C. It is only ever optimal to exercise a call option immediately after an ex-dividend date
D. None of the above
7. What is the number of trading days in a year usually assumed for equities?
A. 365
B. 252
C. 262
D. 272
8. The risk-free rate is 5% and the expected return on a non-dividend-paying stock is 12%. Which
of the following is a way of valuing a derivative?
A. Assume that the expected growth rate for the stock price is 17% and discount the
expected payoff at 12%
B. Assuming that the expected growth rate for the stock price is 5% and discounting the
expected payoff at 12%
C. Assuming that the expected growth rate for the stock price is 5% and discounting the
expected payoff at 5%
D. Assuming that the expected growth rate for the stock price is 12% and discounting the
expected payoff at 5%
9. When there are two dividends on a stock, Black’s approximation sets the value of an American
call option equal to which of the following
A. The value of a European option maturing just before the first dividend
B. The value of a European option maturing just before the second (final) dividend
C. The greater of the values in A and B
D. The greater of the value in B and the value assuming no early exercise
10. Which of the following is measured by the VIX index
A. Implied volatilities for stock options trading on the CBOE
B. Historical volatilities for stock options trading on CBOE
C. Implied volatilities for options trading on the S&P 500 index
D. Historical volatilities for options trading on the S&P 500 index
11. What was the original Black-Scholes-Merton model designed to value?
A. A European option on a stock providing no dividends
B. A European or American option on a stock providing no dividends
C. A European option on any stock
D. A European or American option on any stock
12. A stock provides an expected return of 10% per year and has a volatility of 20% per year. What is
the continuously compounded expected return in one year?
A. 6%
B. 8%
C. 10%
D. 12%
13. An investor has earned 2%, 12% and –10% on equity investments in successive years (annually
compounded). This is equivalent to earning which of the following annually compounded rates
for the three year period.
A. 1.33%
B. 1.23%
C. 1.13%
D. 0.93%
14. Which of the following is NOT true?
A. Risk-neutral valuation assumes that investors are risk neutral
B. Options can be valued based on the assumption that investors are risk neutral
C. In risk-neutral valuation the expected return on all investment assets is set equal to the
risk-free rate
D. In risk-neutral valuation the risk-free rate is used to discount expected cash flows
15. Which of the following is a way of extending the Black-Scholes-Merton formula to value a
European call option on a stock paying a single dividend?
A. Reduce the maturity of the option so that it equals the time of the dividend
B. Subtract the dividend from the stock price
C. Add the dividend to the stock price
D. Subtract the present value of the dividend from the stock price
16. When the Black-Scholes-Merton and binomial tree models are used to value an option on a non-
dividend-paying stock, which of the following is true?
A. The binomial tree price converges to a price slightly above the Black-Scholes-Merton
price as the number of time steps is increased
B. The binomial tree price converges to a price slightly below the Black-Scholes-Merton
price as the number of time steps is increased
C. Either A or B can be true
D. The binomial tree price converges to the Black-Scholes-Merton price as the number of
time steps is increased
17. When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 6%,
the volatility is 20% and the time to maturity is 3 months which of the following is the price of a
European call option on the stock
A. 20N(0.1)-19.7N(0.2)
B. 20N(0.2)-19.7N(0.1)
C. 19.7N(0.2)-20N(0.1)
D. 19.7N(0.1)-20N(0.2)
18. When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 5%,
the volatility is 20% and the time to maturity is 3 months which of the following is the price of a
European put option on the stock
A. 19.7N(-0.1)-20N(-0.2)
B. 20N(-0.1)-20N(-0.2)
C. 19.7N(-0.2)-20N(-0.1)
D. 20N(-0.2)-20N(-0.1)
19. A stock price is 20, 22, 19, 21, 24, and 24 on six successive Fridays. Which of the following is
closest to the volatility per annum estimated from this data?
A. 50%
B. 60%
C. 70%
D. 80%
20. The volatility of a stock is 18% per year. What is the volatility per month?
A. 1.5%
B. 3.0%
C. 5.2%
D. None of the above