Greeks For Multi-asset Options
If the value of a derivative is dependent on two or more underlyings, its Greeks are extended to include the cross-effects between the underlyings.
Correlation delta measures the sensitivity of the derivative's value to a change in the correlation between the underlyings.
Cross gamma measures the rate of change of delta in one underlying to a change in the level of another underlying.
Cross vanna measures the rate of change of vega in one underlying due to a change in the level of another underlying. Equivalently, it measures the rate of change of delta in the second underlying due to a change in the volatility of the first underlying.
Cross volga measures the rate of change of vega in one underlying to a change in the volatility of another underlying.
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“We are only geometricians of matter; the Greeks were, first of all, geometricians in the apprenticeship to virtue.”
—Simone Weil (1909–1943)