A form of gamma that measures the effect of change in delta cash in relative terms. Instead of absolute movements (which are typically captured by plain gamma), gamma cash captures percentage movements. Therefore, it is defined as the change in delta cash for a 1% move in the underlying:

γ_c = δ ×( S_t)²  × 0.01

Delta cash is defined as:

δ_c = δ × S_t

The change in delta for a 1% move in the underlying is:

γ_c = δ × S_t × 0.01

The delta cash after the 1% move in the underlying is:

[δ × S_t × 0.01] × S_t

It follows that gamma cash, or the change in delta cash after the 1% move in the underlying is:

γ_c = [δ × S_t × 0.01] × S_t– [δ × S_t]

γ_c = δ ×( S_t)²  × 0.01