LOS f: Explain the gamma effect on an option's price and delta and how gamma can affect a delta hedge.

Q1. 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)   0.01.

B)   0.10.

C)   1.00.

Q2. How is the gamma of an option defined? Gamma is the change in the:

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

B)   vega as the option price changes.

C)   option price as the underlying security changes.

Q3. When an option’s gamma is higher:

A)   delta will be higher.

B)   a delta hedge will be more effective.

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

Q4. Gamma is the greatest when an option:

A)   is deep in the money.

B)   is at the money.

C)   is deep out of the money.

Q5. Two call options have the same delta but option A has a higher gamma than option B. When the price of the underlying asset increases, the number of option A calls necessary to hedge the price risk in 100 shares of stock, compared to the number of option B calls, is a:

A)   smaller (negative) number.

B)   larger positive number.

C)   larger (negative) number.

LOS f: Explain the gamma effect on an option's price and delta and how gamma can affect a delta hedge. fficeffice" />

Q1. 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)   0.01.

B)   0.10.

C)   1.00.

Correct answer is A)

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

Q2. How is the gamma of an option defined? Gamma is the change in the:

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

B)   vega as the option price changes.

C)   option price as the underlying security changes.

Correct answer is A)

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

Q3. When an option’s gamma is higher:

A)   delta will be higher.

B)   a delta hedge will be more effective.

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

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.

Q4. Gamma is the greatest when an option:

A)   is deep in the money.

B)   is at the money.

C)   is deep out of the money.

Correct answer is B)

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

Q5. Two call options have the same delta but option A has a higher gamma than option B. When the price of the underlying asset increases, the number of option A calls necessary to hedge the price risk in 100 shares of stock, compared to the number of option B calls, is a:

A)   smaller (negative) number.

B)   larger positive number.

C)   larger (negative) number.

Correct answer is A)

For call options larger gamma means that as the asset price increases, the delta of option A increases more than the delta of option B. Since the hedge ratio for calls is – 1/delta, the number of calls necessary for the hedge is a smaller (negative) number for option A than for option B.

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