Baran

 

AIM 8: Define, compute and discuss theta, gamma, vega, and rho for option positions.

1、Which of the following is the best approximation of the gamma of an option if its delta is equal to 0.6 when the price of the underlying security is 100 and 0.7 when the price of the underlying security is 110?

A) 0.00.

B) 0.01.

C) 0.10.

D) 1.00.

Baran

 

The correct answer is B

 

The gamma of an option is computed as follows:

Gamma = change in delta/change in the price of the underlying = (0.7 – 0.6)/(110 – 100) = 0.01

Baran

 

2、How is the gamma of an option defined? Gamma is the change in the:

A) vega as the option price changes.

B) theta as the option price changes.

C) delta as the price of the underlying security changes.

D) option price as the underlying security changes.

Baran

 

The correct answer is C

 

Gamma is the rate of change in delta. It measures how fast the price sensitivity changes as the underlying asset price changes.

Baran

 

3、When an option’s gamma is higher:

A) delta will be lower.

B) delta will be higher. 

C) a delta hedge will perform more poorly over time. 

D) a delta hedge will be more effective. 

Baran

 

The correct answer is C

 

Gamma measures the rate of change of delta (a high gamma could mean that delta will be higher or lower) as the asset price changes and, graphically, is the curvature of the option price as a function of the stock price. Delta measures the slope of the function at a point. The greater gamma is (the more delta changes as the asset price changes), the worse a delta hedge will perform over time.

Baran

 

4、Gamma is the greatest when an option:

A) is deep in the money. 

B) is deep out of the money. 

C) is at the money. 

D) has a shorter maturity.

Baran

 

The correct answer is C

 

Gamma, the curvature of the option-price/asset-price function, is greatest when the asset is at the money.

Baran

 

5、Call and put option values are most sensitive to changes in the volatility of the underlying when:

A) both calls and puts are deep in-the-money.

B) both puts and calls are deep out-of-the-money.

C) calls are deep out-of-the-money and puts are deep in-the-money.

D) both calls and puts are at-the-money.

Baran

 

The correct answer is D

 

Vega measures the sensitivity of the option value to changes in volatility. Vega is at a maximum when calls and put options are at-the-money.