Deck 20: Using the Black-Scholes-Merton Model

Question 1

Since the Black-Scholes-Merton model is rejected when using historical volatilities as input:

A) using implied volatilities transforms the BSM theoretical model into a statistical model
B) implied volatilities enable one to accept the BSM theoretical model
C) one needs to use implied volatilities to delta-hedge an option
D) one needs to use implied volatilities to vega-hedge an option
E) one needs to use implied volatilities to both delta- and gamma-hedge an option

Answer 1

A

Question 2

Which of the following statements is INCORRECT?

A) Option dealers in nineteenth-century London were using a statistical model influenced by insurance industry practices for determining option prices.
B) Option dealers in nineteenth-century New York were selling options primarily for strategic reasons and manipulating option prices.
C) Option dealers in nineteenth-century New York were using "judgment" or "shrewd guessing" to determine option values.
D) Russell Sage's strategy of using put-call parity to charge higher interest rates than the 7 percent maximum allowed by the New York State's usury law was discovered by the authorities and forced Sage to serve jail time.
E) Option trading had more legitimacy in London than in New York.

Answer 2

D

Question 3

The delta for a call option in the Black-Scholes-Merton model is:

A) the number of shares of stock to buy for each written call to eliminate price risk from the resulting position
B) the partial derivative of the option price with respect to the time remaining to maturity
C) the partial derivative of the option price with respect to the volatility
D) the number of shares of the money market account to short for each written call to eliminate price risk from the resulting position
E) the time change in a delta-hedged call option portfolio

Answer 3

A

Question 4

In a delta-hedged call option position over a discrete time interval [t,t + $\Delta$ t]:

A) volatility risk is eliminated
B) small price movement risk is eliminated
C) large price movement risk is eliminated
D) interest rate risk is eliminated
E) both small and large price movement risks are eliminated

Question 5

Calibration in the Black-Scholes-Merton model corresponds to:

A) setting the delta equal to 1/2
B) setting the delta and gamma equal to zero
C) computing an implied volatility
D) setting the interest rate equal to the relevant T-bill rate
E) setting the delta equal to 1

Question 6

A delta for a portfolio of options on the same stock is:

A) the sum of the delta for the individual options times the number of shares of each option
B) the sum of the delta for the individual options times the percentage of each option in the portfolio's value
C) the sum of the delta for the individual options times one minus the percentage of each option in the portfolio's value
D) the sum of the delta for the individual options divided by the number of shares of each option
E) cannot be computed if the options have different strikes

Question 7

A portfolio which has a delta value of -0.25 is:

A) a bullish portfolio
B) a neutral portfolio
C) a bearish portfolio
D) a high-volatility portfolio
E) None of these answers are correct.

Question 8

Using a Taylor series expansion of the Black-Scholes-Merton model,one can hedge the following risks in an option and stock portfolio:

A) volatility risk
B) small and large stock price risk
C) small stock price risk and interest rate risk
D) small stock price risk and volatility risk
E) small and large stock price risk and volatility risk

Question 9

The Black-Scholes-Merton model's implied volatility is:

A) the market's estimate of the future value of the stock's random volatility over the option's life
B) the volatility that equates the BSM model price to the market price,if all other inputs are known
C) the market's estimate of the future value of the stock's random volatility over an infinitesimal time interval
D) the market's estimate of the stock's random volatility over an infinitesimal time interval beginning when the option matures
E) another name for estimating the volatility using historical stock price data

Question 10

Gamma hedging is needed when hedging in the Black-Scholes-Merton model because:

A) there is volatility risk in holding the option
B) there is interest rate risk in holding the option
C) when hedging,one can only trade discretely in time and not continuously
D) when hedging,the interest rate is not constant
E) there is time decay in holding the option

Question 11

Which of the following statements is INCORRECT?

A) The VIX was introduced during the 1990s to measure the market's expectation of the 30-day volatility implied by at-the-money S&P 100 Index (OEX)option prices.
B) During the early 2000s,VIX index was modified to represent an expected volatility instead of an implied volatility.
C) VIX is also known as the "fear index" because it has become a widely watched barometer of stock market volatility,reflecting investor anxiety.
D) The VIX is a measure of the level of the S&P 100 stock market index.
E) The VIX tends to increase during financial crises.

Question 12

Which of the following Black-Scholes-Merton model inputs are parameters and risks?

A) Parameters (r, $\sigma$ ,K,T),risk (S)
B) Parameters (r,K,T),risks (S,r)
C) Parameters (r,K,T),risks (S, $\sigma$ )
D) Parameters (K,T),risks (S,r, $\sigma$ )
E) Parameter (K),risks (S,r, $\sigma$ ,T)

Question 13

The Black-Scholes-Merton model is:

A) empirically validated because implied volatilities match market-to-model prices
B) rejected because implied volatilities are not constant across strikes and maturities
C) empirically validated because calibrated BSM models are used on Wall Street
D) empirically validated because BSM theory enabled successful delta and gamma hedging
E) is rejected because implied volatilities can only be computed for at-the-money options

Question 14

Which of the following statements is correct?

A) Theoretical models capture correlations in past market data.
B) Statistical models include cause and effect.
C) Theoretical models include cause and effect.
D) Statistical models capture structural shifts.
E) Statistical models dominate theoretical models because they use market data.

Question 15

Which of the following is true with respect to hedging in the Black-Scholes-Merton model?

A) One can hedge interest rate risk using rho.
B) One can hedge volatility rate risk using vega.
C) One can hedge time decay risk using theta.
D) One can hedge small price risk using delta.
E) One can hedge large price risk using delta.

Question 16

The Black-Scholes-Merton model is a:

A) theoretical model
B) statistical model
C) econometric model
D) equilibrium model
E) None of these answers are correct.

Question 17

In a delta- and gamma-hedged call option position over a discrete time interval [t,t + $\Delta$ t]:

A) volatility risk is eliminated
B) small price movement risk is eliminated
C) large price movement risk is eliminated
D) interest rate risk is eliminated
E) both small and large price movement risk are eliminated