What are vanna, vomma, and charm, and why do dealers care about them?

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AcadiFi · Accepted Answer

Second-order Greeks capture cross-partial sensitivities: vanna = dDelta/dSigma = dVega/dSpot (how delta changes with vol, or vega with spot); vomma (volga) = dVega/dSigma (vega convexity); charm = dDelta/dTime (delta decay). These matter when first-order hedges drift as market conditions change. Vanna is critical for FX and equity options when skew/smile shifts: a stock rallies and implied vol drops simultaneously, changing delta even if spot-vega hedged. Vomma measures how vega changes as vol moves—large for OTM options near the wings of the smile, negligible at-the-money. Charm captures overnight delta decay, important for delta-hedged books held through weekends. ```mermaid flowchart TB D[Delta] --> V[Vanna
dDelta/dSigma] V_EGA[Vega] --> V V_EGA --> VG[Vomma
dVega/dSigma] D --> CH[Charm
dDelta/dTime] ``` For Luminara's EUR/USD book, a short 1-month ATM straddle has vanna ≈ 0, vomma ≈ 0 (peak gamma/vega at ATM), but charm is large (gamma peaks as expiry approaches). A short 3-month 25-delta risk reversal has significant vanna (sensitive to skew) and vomma (sensitive to vol-of-vol). Hedging: vanna is hedged with risk reversals (long call + short put at symmetric deltas), vomma with butterflies or strangles, charm is typically let run but managed by rebalancing delta frequency. Sophisticated dealers run Greek-by-Greek P&L attribution to attribute daily moves to each risk factor, flagging unintended exposures.

What are vanna, vomma, and charm, and why do dealers care about them?

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