Deck 5: Option Pricing Models: the Black-Scholes-Merton Model

Question 1

Which of the following characteristics of the Black-Scholes-Merton model is not correct?

A)it is a discrete time model
B)it is the limit of the binomial model
C)it is a continuous time model
D)it gives the price of a European option
E)none of the above

Answer 1

A

Question 2

The relationship between the volatility and the time to expiration is called the

A)volatility smile
B)volatility skew
C)term structure of volatility
D)theta
E)none of the above

Answer 2

C

Question 3

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

A)higher than 0.28
B)lower than 0.28
C)0.28
D)lower than the risk-free rate
E)none of the above

Answer 3

A

Question 4

Which of the following variables in the Black-Scholes-Merton option pricing model is the most difficult to obtain?

A)the volatility
B)the risk-free rate
C)the stock price
D)the time to expiration
E)the exercise price

Question 5

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
² = 0.15
No dividends are expected.
Use this information to answer questions
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. )

A)0.7580
B)0.2420
C)-0.2480
D)-0.6628
E)none of the above

Question 6

Which of the following statements is true about the relationship between the option price and the risk-free rate?

A)a call price is nearly linear with respect to the risk-free rate
B)a call price is highly sensitive to the risk-free rate
C)the risk-free rate affects a call but not a put
D)the risk-free rate does not affect a call price
E)none of the above

Question 7

Which of the following "Greeks" is not a measure of the option's sensitivity to a change in one of its input values?

A)delta
B)gamma
C)rho
D)theta
E)sigma

Question 8

Which of the following statements about the delta is not true?

A)it ranges from zero to one
B)it converges to zero or one at expiration
C)it is given by N(d1)in the Black-Scholes-Merton model
D)it changes slowly near expiration if the option is at-the-money
E)none of the above

Question 9

If the simple return on a Treasury bill is 8.5 percent,the risk-free rate in the Black-Scholes-Merton model is

A)8.77 percent
B)8.93 percent
C)8.55 percent
D)8.20 percent
E)none of the above

Question 10

The binomial price will theoretically equal the Black-Scholes-Merton price under which of the following conditions?

A)when the number of time periods is large
B)when the option is at-the-money
C)when the option is in-the-money
D)when the option is out-of-the-money
E)none of the above

Question 11

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
² = 0.15
No dividends are expected.
Use this information to answer questions
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. )

A)5.35
B)1.10
C)4.73
D)6.50
E)none of the above

Question 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
² = 0.15
No dividends are expected.
Use this information to answer questions
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. )

A)-3.02
B)0.046
C)-0.792
D)4.67
E)none of the above

Question 13

Which of the following statements about the Black-Scholes-Merton model is not true?

A)decreasing the volatility lowers the call price
B)the expected stock price plays a role in the model
C)the risk-free rate is continuously compounded
D)the model is consistent with put-call parity
E)none of the above

Question 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
² = 0.15
No dividends are expected.
Use this information to answer questions
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. )

A)22.60
B)19.65
C)23.00
D)21.99
E)none of the above

Question 15

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
² = 0.15
No dividends are expected.
Use this information to answer questions
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. )

A)0.85
B)8.64
C)2.35
D)4.88
E)none of the above

Question 16

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
² = 0.15
No dividends are expected.
Use this information to answer questions
If the actual call price is 3.79,the implied standard deviation is

A)0.25
B)greater than 0.25
C)less than 0.25
D)infinite
E)none of the above

Question 17

What is the reason for executing a gamma hedge?

A)the volatility can change
B)the stock price can make a large move
C)the stock price moves are too small for a delta hedge to work
D)there is no true risk-free rate
E)none of the above

Question 18

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
² = 0.15
No dividends are expected.
Use this information to answer questions
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. )

A)17.75
B)20.75
C)20.00
D)20.80
E)none of the above

Question 19

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
² = 0.15
No dividends are expected.
Use this information to answer questions
Suppose you feel that the call is overpriced.What strategy should you use to exploit the apparent misvaluation? (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. )

A)buy 791 shares,sell 1,000 calls
B)buy 705 shares,sell 1,000 calls
C)sell short 791 shares,buy 1,000 calls
D)sell short 705 shares,buy 1,000 calls
E)none of the above

Question 20

Which of the following assumptions of the Black-Scholes-Merton model is not correct?

A)the stock volatility is constant
B)the stock return follows a normal distribution
C)there are no transaction costs
D)there are no taxes
E)none of the above

Question 21

What happens when the volatility is zero in the Black-Scholes-Merton model?

A)the option price converges to either zero or the lower bound
B)the option price converges to the intrinsic value
C)the option automatically expires out of the money
D)the gamma and delta converge
E)none of the above

Question 22

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

Question 23

Which of the following is not correct about a call's gamma?

A)it is the same as a put's gamma
B)it is large when the call is at-the-money
C)it can be viewed as a measure of the risk of the delta
D)it is a source of risk that can be hedged only by using another option
E)none of the above

Question 24

Which of the following statements about the volatility is not true?

A)the implied volatility often differs across options with different exercise prices
B)the implied volatility equals the historical volatility if the option is correctly priced
C)the implied volatility is determined by trial and error
D)the implied volatility is nearly linearly related to the option price
E)none of the above

Question 25

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

Question 26

Which of the following statements is incorrect about the historical volatility?

A)if used in the Black-Scholes-Merton model,it gives the current market price
B)it is based on the volatility of the log return on the stock
C)it requires a sample of recent returns
D)it should be converted to an annualized volatility
E)none of the above

Question 27

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

Question 28

The option's rate of time value decay is represented by its theta.

Question 29

The option's delta is approximately the change in the option price for a change in the stock price.

Question 30

The Black-Scholes-Merton model assumes that the volatility does not change throughout the option's life.

Question 31

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

Question 32

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

Question 33

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

Question 34

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.

Question 35

The relationship between the option price and the exercise price is called

A)the gamma
B)the vega
C)the omega
D)the zeta
E)none of the above

Question 36

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

Question 37

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

Question 38

An option's gamma represents the risk of the delta changing.

Question 39

When the risk-free rate is zero,the Black-Scholes formula converges to the intrinsic value.

Question 40

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

Question 41

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

Question 42

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

Question 43

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

Question 44

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

Question 45

The volatility smile is the relationship between implied volatility and historical volatility.

Question 46

Vega captures the combined effects of time decay and volatility.

Question 47

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

Question 48

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

Question 49

The option's sensitivity to an interest rate change is called rho.

Question 50

The historical volatility is the same value as the implied volatility.