What is Vanna in Options Trading?
Vanna is a second-order Greek that couples delta and vega: it tells you how your directional exposure shifts when the implied vol surface moves.
Definition
Vanna is ∂²V/∂S∂σ — the cross-partial of option value with respect to spot and volatility. It can be read two equivalent ways: how much your delta changes per 1-vol-point move in implied volatility, or how much your vega changes per 1-point move in spot. Vanna is positive for OTM calls (delta rises when vol rises) and for OTM puts on the underside in absolute terms. Risk-reversals (long call / short put or vice versa) are nearly pure vanna trades — they are designed to express a view on skew without taking ATM vega exposure. On dealer-positioning analysis, vanna flow explains why a vol crush during a rally accelerates the rally itself: as vol drops, OTM-call deltas drop, and dealers who were short those calls have to buy back hedges.
Why it matters & how it's calculated
Vanna is one of the three main second-order Greeks (with gamma and volga). Numerically, under a standard pricing model, vanna = ∂Δ/∂σ = ∂Vega/∂S = −φ(d₁) · d₂ / σ. The sign of vanna depends on moneyness: it changes sign roughly at-the-money. For dealer positioning models, vanna is critical because real vol surfaces are not static — when SPX rallies 1%, the entire surface typically drops by some amount (the spot-vol correlation), which mechanically forces dealers to re-hedge. This is what desks call "vanna flow." During the 2018 Volmageddon, vanna-flow models predicted exactly the kind of buy-the-rip / sell-the-dip behaviour we observed in dealer hedging during the unwind. On a vol book, vanna is also why you have to think in "skew vega" not just ATM vega — a portfolio that is long downside vol and short upside vol has zero ATM vega but huge vanna exposure, and will P&L significantly on any skew flattening.
Formula
Vanna = ∂Δ/∂σ = ∂Vega/∂S = −φ(d₁) · d₂ / σ
Worked example
You own 100 SPX 25-delta calls 3 months out. Each has vanna ≈ +0.005 (delta per vol point). If the entire vol surface drops 2 points overnight on a Fed-induced calm, each call's delta drops by 0.01. Your aggregate delta drops by 100 × 100 × 0.01 = 100 deltas — meaning your portfolio just became 100 SPX-equivalent shares less long, even though spot did not move. You'll need to buy back those deltas to stay hedged.
Related concepts
Learn this in depth on a live desk
These are the building blocks the desk uses every day. The 180+ hour Whop course shows you how they fit together on a real book — and the book walks you through the framework end-to-end.