Explain 'gamma' and describe how it influences delta hedging as the underlying moves.

• A. Gamma is the sensitivity of delta to volatility changes.
• B. Gamma is the rate of change of delta with respect to the underlying price, but not measured per unit.
• C. Gamma is the rate of change of delta per 1 unit move in the underlying.
• D. Gamma is the probability that the option finishes in the money.

Answer: (C)

Gamma measures how rapidly delta changes as the underlying price moves. It is the derivative of delta with respect to the underlying price, equivalently the second derivative of the option’s value with respect to the underlying. In delta hedging, you aim to offset the option’s delta with a position in the underlying, but delta itself shifts as S changes. For a small move in the underlying, the new delta is approximately the old delta plus gamma times the move in the underlying. So to stay hedged, you adjust the hedge by roughly gamma times the underlying move. Higher gamma means the delta changes more for a given price move, so hedges must be rebalanced more frequently; this is especially true for at-the-money options and as expiration nears, where gamma tends to be larger. Long options have positive gamma, so delta moves in the same direction as the stock price, increasing the hedge’s sensitivity as the underlying moves.