Deck 19: The Black-Scholes-Merton Model

Question 1

The following input is not needed to solve the option price in the Black-Scholes-Merton framework:

A) the asset's risk premium
B) the asset price
C) the time to maturity
D) the risk-free rate of interest
E) the strike price

Answer 1

A

Question 2

Which statement about the argument underlying the Black-Scholes-Merton model is INCORRECT?

A) The argument utilizes a practice common among option writers in nineteenth-century London: hedge an option position with an opposing stock trade.
B) The argument combines and solves the pricing and hedging problem in one stroke.
C) The argument assumes that call and underlying stock prices are positively correlated.
D) The argument combines the call and the underlying stock to form a riskless portfolio that is assumed to grow at the risk-free rate.
E) The argument assumes that all traders are risk-neutral,and therefore one can value the option by taking expected discounted values.

Answer 2

E

Question 3

If the stock pays a dividend at the continuously compounded rate of $\delta$ = 0.01 per year,then the Black-Scholes-Merton model gives the price of a European call as:

A) $5.75
B) $5.99
C) $9.46
D) $9.88
E) None of these answers are correct.

Answer 3

$5.75

Question 4

If the stock pays a dividend at the continuously compounded rate of $\delta$ =0.01 per year,then the Black-Scholes-Merton model gives the price of a European put as:

A) $5.75
B) $5.99
C) $8.66
D) $10.34
E) None of these answers are correct.

Question 5

The stock market has been fluctuating widely,and a "market guru" declares in his newsletter that the traditional Black-Scholes-Merton option pricing model is no longer valid.Instead,he says traders should use the following model for computing an option's price: take the average of the highest and the lowest prices for each of the previous seven trading days.If you use this pricing model,then you are:

A) a mathematical modeler
B) a statistical modeler
C) a "lottery" buyer
D) a day trader
E) None of these answers are correct.

Question 6

The SINDY index is currently at I = 10,100.European options on SINDY have a strike price K =$10,000 and mature in T = 90 days.The risk-free interest rate r = 5 percent per year.SINDY has a dividend yield $\delta$ = 2 percent per year and an implied volatility of $\sigma$ = 20 percent per year.Then the Black-Scholes-Merton model gives a call option price of:

A) $314.18
B) $430.39
C) $487.03
D) $516.76
E) None of these answers are correct.

Question 7

The first successful option pricing model was built by:

A) Louis Bachelier
B) James Boness and Case Sprenkle
C) Paul Samuelson
D) Fischer Black,Myron Scholes,and Robert Merton
E) Sheen Kassouf and Edward Thorp

Question 8

The Black-Scholes-Merton model assumes that the stock price follows:

A) a normal distribution
B) a lognormal distribution
C) a binomial distribution
D) an additive distribution
E) a uniform distribution

Question 9

The assumptions underlying the Black-Scholes-Merton model for pricing European options do NOT include:

A) no market frictions
B) no credit risk
C) competitive and well-functioning markets
D) no interest rate uncertainty
E) trading only at discrete time intervals

Question 10

Which of the following statements is INCORRECT about asset price bubbles?

A) A price bubble happens when an asset's price substantially deviates from its intrinsic or fundamental value.
B) A price bubble implies the existence of arbitrage and they are excluded by the no arbitrage assumption.
C) Price bubbles cannot be accommodated in the Black-Scholes-Merton model because the assumption that the stock price follows a lognormal distribution excludes bubbles.
D) A price bubble can happen when the assumption "competitive and well-functioning market" fails to hold.
E) In the presence of price bubbles,many of the standard results of option pricing are no longer valid.

Question 11

A modification to the BSM option pricing model developed by Robert Merton (1973)was formulated to price:

A) American options on equity with dividends
B) American options on equity with no dividends
C) European options on equity with a known dividend yield
D) European options on equity with no dividends
E) European options on commodity futures

Question 12

Which of the following statements is INCORRECT?

A) An option's delta measures the change in the option's value when there is a small change in the underlying stock price.
B) The delta of a call option lies between 0 and 1.
C) The delta of a put option lies between -1 and 0.
D) An option's gamma is the change in the option's delta when there is a small change in the underlying stock price.
E) The gamma for otherwise identical European put and call options on the same stock are different.

Question 13

A stock's current price S is $100.Its return has a volatility of $\sigma$ = 25 percent per year.European call and put options trading on the stock have a strike price of K = $105 and mature after T = 0.5 years.The continuously compounded risk-free interest rate r is 5 percent per year.

-The Black-Scholes-Merton model gives the price of the European put as:

A) $5.79
B) $5.99
C) $8.40
D) $9.88
E) None of these answers are correct.

Question 14

If a put option has a delta close to -0.5,then the call is likely to be:

A) deeply in-the-money
B) at-the-money or the stock price is close to the strike price
C) deeply out-of-the-money
D) either deeply in-the-money or deeply out-of-the money
E) None of these answers are correct.

Question 15

Identify the correct statement.A stock's historic volatility is obtained by:

A) computing the standard deviation of stock prices
B) computing the standard deviation of price relatives of the stock prices
C) computing the standard deviation of logarithm price relatives
D) computing volatility as implied by market-traded option prices
E) None of these answers are correct.

Question 16

A stock's current price S is $100.Its return has a volatility of $\sigma$ = 25 percent per year.European call and put options trading on the stock have a strike price of K = $105 and mature after T = 0.5 years.The continuously compounded risk-free interest rate r is 5 percent per year.

-The Black-Scholes-Merton model gives the price of the European call as:

A) $5.99
B) $8.26
C) $10.00
D) $12.34
E) None of these answers are correct.

Question 17

Suppose that you have computed a stock return's variance with weekly data.To convert this to an annual variance,you need to use the adjustment:

A) Variance (Annual)= Variance (Weekly)*12
B) Variance (Annual)= Variance (Weekly)*52
C) Variance (Annual)= Variance (Weekly)* 250
D) Variance (Annual)=Variance (Weekly)*260
E) None of these answers are correct.

Question 18

When pricing options,the following input is the hardest to estimate the:

A) interest rate
B) dividend yield
C) volatility
D) strike price
E) yield to maturity

Question 19

The model developed by Fischer Black and Myron Scholes (1973)was initially used for pricing:

A) an American option on equity with dividends
B) an American option on equity with no dividends
C) a European option on commodity with a known dividend yield
D) a European option on equity with no dividends
E) a European option on an index

Question 20

Identify the correct sentence.In the Black-Scholes-Merton model (1973):

A) the European option price can be computed as its discounted expected payoff using the actual probabilities and the risk-free rate
B) the European option price can be computed as its discounted expected payoff using the actual probabilities and the expected return
C) the European option price can be computed as its discounted expected payoff using the pseudo-probabilities and the expected return
D) the European option price can be computed as its discounted expected payoff using the pseudo-probabilities and the risk-free rate
E) None of these answers are correct.

Question 21

Which of the following statements is INCORRECT?

A) The Black-Scholes-Merton model can be used to price an American call option on a stock paying known dollar dividends.
B) The binomial model can be used to price an American call option in the presence of known dividends.
C) The Black-Scholes-Merton model can be used to price a European call option on a stock with a known dividend yield.
D) The Black-Scholes-Merton model can be used to price a European put option on a stock paying known dollar dividends.
E) None of these answers are correct.

Question 22

Which of the following statements is INCORRECT?

A) An American option's price can be determined by the Black-Scholes-Merton model.
B) An American option's price can be determined by a multiperiod binomial option pricing model.
C) An American option's price can be determined by numerically solving the underlying partial differential equation.
D) An American option's price can be determined by using Monte Carlo simulation techniques.
E) None of these answers are correct.

Question 23

A European call on the euro matures after T =0 90 days.The call pays on the maturity 100[S_A (T )-1.20] dollars if it ends in-the-money,zero otherwise,where 100 is the contract multiplier and $1.20 is the strike price K.The euro's volatility $\sigma$ is 15 percent per year.Today's spot exchange rate S_A is $1.3 per euro (in American terms).The continuously compounded annual risk-free interest rates are r = 4 percent in the United States (domestic)and r_E = 3 percent in the Eurozone.Then the Black-Scholes-Merton model gives a call option price of:

A) $0.62
B) $0.71
C) $10.56
D) $10.84
E) None of these answers are correct.