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:
γc = δ ×( St)2 × 0.01
Delta cash is defined as:
δc = δ × St
The change in delta for a 1% move in the underlying is:
γc = δ × St × 0.01
The delta cash after the 1% move in the underlying is:
[δ × St × 0.01] × St
It follows that gamma cash, or the change in delta cash after the 1% move in the underlying is:
γc = [δ × St × 0.01] × St– [δ × St]
γc = δ ×( St)2 × 0.01
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