[2008]Topic 19: The Black-Scholes-Merton Model相关习题

Baran

 

AIM 3: List, define and relate the assumptions underlying the Black-Scholes-Merton model.

1、Which of the following is NOT one of the assumptions of the Black-Scholes-Merton option-pricing model?

A) There are no cash flows over the term of the options. 

B) The volatility is known and remains constant over the term of the option.  

C) The yield curve for risk-free assets is fixed over the term of the option.  

D) There are no taxes and transactions costs are zero for options and arbitrage portfolios. 

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Baran

 

3、If we use four of the inputs into the Black-Scholes-Merton option-pricing model and solve for the asset price volatility that will make the model price equal to the market price of the option, we have found the:

A) implied volatility.  

B) historical volatility.  

C) market volatility.  

D) option volatility.

Baran

 

The correct answer is A

 

The question describes the process for finding the expected volatility implied by the market price of the option.

Baran

 

4、Which of the following is TRUE for an option's price? An option's price is:

A) a decreasing function of the underlying asset's volatility. 

B) unaffected by changes in the underlying asset's volatility. 

C) an increasing function of the underlying asset's volatility. 

D) a decreasing function of the underlying asset's volatility when it has a long time remaining until expiration and an increasing function of its volatility if the option is close to expiration.

Baran

 

The correct answer is C

 

Since an option has limited risk but significant upside potential, its value always increases when the volatility of the underlying asset increases.

Baran

 

AIM 7: List and discuss the various methods that estimate future volatility.

1、The implied volatility of interest rates can be best computed using the market price of an:

A) interest rate forward contract. 

B) interest rate futures contract. 

C) interest rate call option contract. 

D) S& 500 option contract.

Baran

 

The correct answer is D

 

Implied volatility of interest rates can be best computed using interest rate option contracts. Forward or futures contract pricing models do not have interest rate volatility as an input. S& 500 option contracts have the volatility of the S& 500 index (and not interest rates) as an input.

Baran

 

2、Which of the following methods is NOT used for estimating volatility inputs for the Black-Scholes model?

A) Using long term historical data. 

B) Using the most current historical data. 

C) Using exponentially weighted historical data. 

D) Models of changing volatility.

Baran

 

The correct answer is D

 

The volatility is constant in the Black-Scholes model.