Gamma exposure, sometimes referred to as dollar gamma, measures the second order price sensitivity of an option or portfolio to changes in the price of an underlying security.
Mathematically, gamma exposure is equal to half the gamma of the portfolio multiplied by the price of the underlying security squared. For an underlying with price S, then, we have:
For an option with price V, the second order approximation to the change in the price of an option due to a change in the price of the underlying is:
By multiplying and dividing by S, we can express the equation in terms of delta and gamma exposures:
In other words, to a second order approximation, the change in the value of an option is equal to the dollar delta multiplied by the percentage change in the value of the underlying security plus the dollar gamma multiplied by the percentage change in the underlying security squared.