gamma exposure (gex)

When we say that options are convex instruments, we are, in part, referring to their gamma (𝛄).

Because it is uncertain whether an option will expire in-the-money, the delta of an option fluctuates with time and with the price of the underlying. If delta is the speed at which an option will gain or lose value with a $1 change in the underlying, gamma is the acceleration. 100 × 𝛄 × OI tells us how many additional shares would be required to be delta-hedged given a $1 change in the underlying. As with dex, the capital required for these additional shares is given to us by multiplying by the share price. To obtain a standardized metric directly proportional to percentage moves in the underlying, we multiply the standard $1 price change by the underlying share price × 1% (S × 0.01). Putting it all together: 100 × 𝛄 × OI × share price × share price × 1% (100 × Γ × OI × S² × 0.01).

Whether your delta is positive or negative, the acceleration of your delta will be the same. Thus, gamma is positive for all long (bought) options and negative for all short (sold) options. We view the result ladder-style, on a strike by strike basis. Call gex and put gex can be netted out for cleaner visualization. As with dex, performing this operation for all strikes and summing the result gives us the capital required to hedge the entire complex given a 1% move in the underlying. (cf. Perfiliev)