How does DvegaDspot relate to vanna and why is it useful?

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AcadiFi · Accepted Answer

DvegaDspot is the partial derivative of vega with respect to spot. By the symmetry of mixed partial derivatives (Clairaut's theorem), DvegaDspot equals DdeltaDvol, which is vanna. So yes, DvegaDspot is vanna viewed from the opposite angle: one tells you how vega changes when spot moves, the other tells you how delta changes when vol moves, and numerically they are identical.

On an FX book at a desk like Marlbrook Currency Advisors, a trader reads DvegaDspot when asking: if spot moves up 1%, how does my vega change? Suppose the book has vega of 18,000 and DvegaDspot equal to 2,100 per 1% spot. A 2% spot rally shifts vega to roughly 22,200, materially changing the vol hedge required. Meanwhile, the same trader reading the position as vanna asks: if vol moves up 1 point, how does my delta shift? Both questions drive the same hedge rebalance, so desks can choose either lens.

The practical use is rebalancing: when spot trends strongly, DvegaDspot tells you that your vega exposure is silently drifting, which matters for vega limits and for the vol P&L explain. For CFA candidates, recognize that Greeks are partial derivatives in a multi-variable function, and mixed partials obey symmetry, which is why two-named Greeks appear often in options literature. This symmetry also means hedging one cross-risk automatically hedges the other.

How does DvegaDspot relate to vanna and why is it useful?

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