［2008］Topic 20: Greek Letters相关习题 option

Baran

AIM 1: Discuss and assess the risks associated with naked and covered option positions.

 

1、As an option approaches expiration, the value of rho for a put option:

A) decreases and tends toward zero.
 
B) decreases and tends toward negative infinity.
 
C) increases and tends toward infinity.
 
D) increases and tends toward zero.

Baran

The correct answer is D

Rho values for put options are always negative and approach zero as the option nears maturity.

Baran

 

AIM 3: Define delta hedging for an option, forward, and futures contracts.

 

1、Ronald Franklin, CFA, has recently been promoted to junior portfolio manager for a large equity portfolio at Davidson-Sherman (DS), a large multinational investment-banking firm. He is specifically responsible for the development of a new investment strategy that DS wants all equity portfolio managers to implement. Upper management at DS has instructed its portfolio managers to begin overlaying option strategies on all equity portfolios. The relatively poor performance of many of their equity portfolios has been the main factor behind this decision. Prior to this new mandate, DS portfolio managers had been allowed to use options at their own discretion, and the results were somewhat inconsistent. Some portfolio managers were not comfortable with the most basic concepts of option valuation and their expected return profiles, and simply did not utilize options at all. Upper management of DS wants Franklin to develop an option strategy that would be applicable to all DS portfolios regardless of their underlying investment composition. Management views this new implementation of option strategies as an opportunity to either add value or reduce the risk of the portfolio.

Franklin gained experience with basic options strategies at his previous job. As an exercise, he decides to review the fundamentals of option valuation using a simple example. Franklin recognizes that the behavior of an option's value is dependent on many variables and decides to spend some time closely analyzing this behavior. His analysis has resulted in the information shown in Exhibits 1 and 2 for European style options.

Exhibit 1: Input for European Options
Stock Price (S)	100
Strike Price (X)	100
Interest Rate (r)	0.07
Dividend Yield (q)	0.00
Time to Maturity (years) (t)	1.00
Volatility (Std. Dev.)(Sigma)	0.20
Black-Scholes Put Option Value	$4.7809

 

Exhibit 2: European Option Sensitivities
Sensitivity	Call	Put
Delta	0.6736	-0.3264
Gamma	0.0180	0.0180
Theta	-3.9797	2.5470
Vega	36.0527	36.0527
Rho	55.8230	-37.4164

Franklin wants to know if the option sensitivities shown in Exhibit 2 have minimum or maximum bounds. Which of the following are the minimum and maximum bounds, respectively, for the put option delta?

A) -1 and 1.

B) -1 and 0.

C) -1 and no maximum bound.

D) There are no minimum or maximum bounds.

Baran

 

The correct answer is B

 

The lower bound is achieved when the put option is far in the money so that it moves exactly in the opposite direction as the stock price. When the put option is far out of the money, the option delta is zero. Thus, the option price does not move even if the stock price moves since there is almost no chance that the option is going to be worth something at expiration.

Baran

 

2、Ronald Franklin, CFA, has recently been promoted to junior portfolio manager for a large equity portfolio at Davidson-Sherman (DS), a large multinational investment-banking firm. He is specifically responsible for the development of a new investment strategy that DS wants all equity portfolio managers to implement. Upper management at DS has instructed its portfolio managers to begin overlaying option strategies on all equity portfolios. The relatively poor performance of many of their equity portfolios has been the main factor behind this decision. Prior to this new mandate, DS portfolio managers had been allowed to use options at their own discretion, and the results were somewhat inconsistent. Some portfolio managers were not comfortable with the most basic concepts of option valuation and their expected return profiles, and simply did not utilize options at all. Upper management of DS wants Franklin to develop an option strategy that would be applicable to all DS portfolios regardless of their underlying investment composition. Management views this new implementation of option strategies as an opportunity to either add value or reduce the risk of the portfolio.

Franklin gained experience with basic options strategies at his previous job. As an exercise, he decides to review the fundamentals of option valuation using a simple example. Franklin recognizes that the behavior of an option's value is dependent on many variables and decides to spend some time closely analyzing this behavior. His analysis has resulted in the information shown in Exhibits 1 and 2 for European style options.

Exhibit 1: Input for European Options
Stock Price (S)	100
Strike Price (X)	100
Interest Rate (r)	0.07
Dividend Yield (q)	0.00
Time to Maturity (years) (t)	1.00
Volatility (Std. Dev.)(Sigma)	0.20
Black-Scholes Put Option Value	$4.7809

 

Exhibit 2: European Option Sensitivities
Sensitivity	Call	Put
Delta	0.6736	-0.3264
Gamma	0.0180	0.0180
Theta	-3.9797	2.5470
Vega	36.0527	36.0527
Rho	55.8230	-37.4164

Which of the following is the best estimate of the change in the put option when the underlying equity increases by $1?

A) -$3.61.

B) -$0.33.

C) -$0.37.

D) $0.67.

Baran

 

The correct answer is B

 

The correct value is simply the delta of the put option in Exhibit 2.

The incorrect value -$3.61 represents the change due to the volatility divided by 10 multiplied by –1.
The incorrect value -$0.37 calculates the change by dividing the short-term interest rate divided by 100.
The incorrect value $0.67 represents the change in the call option.

Baran

 

Franklin computes the rate of change in the European put option delta value, given a $1 increase in the underlying equity. Using the information in Exhibits 1 and 2, which of the following is the closest to Franklin's answer?

A) -0.3264.

B) 0.6736.

C) 0.0180.

D) 36.0527.

Baran

 

The correct answer is C

The correct value 0.0180 is referred to as the put option's Gamma.

The incorrect value -0.3264 is the delta of the put option.

The incorrect value 0.6736 is the call option's delta.

The incorrect value 36.0527 is the put option's Vega.

Baran

 

3、Which of the following is the best interpretation of delta for an option? Delta is the change in the option price for:

A) an instantaneous change in interest rates.

B) an instantaneous change in price of the underlying stock.

C) a change in the time until expiration of the option.

D) an instantaneous change in the volatility of the underlying stock.

Baran

 

The correct answer is B

 

Delta is the slope of the price function of the call option payoff diagram.