Vanna and Volga: The Second-Order Greeks

Vanna and volga are second-order Greeks that describe how the primary Greeks interact with each other. They're less intuitive than delta and theta, but they explain significant pricing behavior that first-order Greeks alone can't capture—especially around volatility events and at extreme strikes.

What Is Vanna?

Vanna = ∂Delta/∂Volatility = ∂Vega/∂Spot

Vanna measures two equivalent things:

  • How much delta changes when implied volatility changes
  • How much vega changes when the stock price changes

    • These are mathematically identical (cross-partial derivative), which is why vanna connects directional exposure to volatility exposure.

    Practical meaning: When IV rises, vanna tells you how much your delta will shift. For OTM calls, vanna is positive—rising IV increases their delta (they become more sensitive to stock movement because the market assigns higher probability to reaching the strike). For OTM puts, vanna is negative—rising IV makes their delta more negative.

    Example: You hold OTM TSLA $280 calls (TSLA at $250) with a delta of 0.20 and vanna of 0.03. If TSLA's IV jumps 5 points (from 50% to 55%), your delta shifts by approximately 0.03 × 5 = 0.15. Your calls now have 0.35 delta—they went from mildly sensitive to meaningfully directional, purely from a volatility change.

    Vanna's Market Impact

    Vanna explains why volatility spikes cause outsized moves. When VIX spikes:

  • OTM put deltas increase in magnitude (more negative)
  • Market makers who are short those puts must sell more stock to hedge
  • This selling pressure pushes prices lower, further increasing put deltas
  • The cycle feeds on itself

    • This vanna-driven feedback loop contributes to the severity of market selloffs. The combination of gamma hedging (buying low, selling high) and vanna hedging (selling into IV spikes) creates complex dynamics that institutional desks model carefully.

    On the upside: When IV collapses (post-earnings calm, VIX crash), OTM call deltas shrink (vanna effect). Dealers who were long stock to hedge those calls sell shares, which can dampen rallies.

    What Is Volga?

    Volga = ∂Vega/∂Volatility (also called vomma or vega convexity)

    Volga measures how much an option's vega changes when implied volatility itself changes. It describes the curvature of the vega response.

    Practical meaning: A high-volga option's vega increases as IV rises. This means the option becomes increasingly sensitive to further IV changes—it's convex in volatility. A low-volga option's vega is stable regardless of IV level.

    Where volga is highest: Deep OTM and deep ITM options. The intuition: when IV is low, a far OTM option has near-zero vega (it's essentially worthless). When IV spikes dramatically, that option suddenly has real value, and its vega skyrockets. This large change in vega from a change in IV is volga.

    ATM options have relatively low volga because their vega is already near maximum and doesn't change much with IV shifts.

    Volga in Practice

    Tail risk hedging: Portfolio insurance (deep OTM puts) has high volga. In normal markets, these puts are cheap with low vega. When a crisis hits and IV explodes, their vega spikes (volga effect), making them increasingly sensitive to further IV increases. This convexity is exactly what tail risk hedgers pay for—the protection accelerates when you need it most.

    Volatility-of-volatility pricing: Volga drives the pricing of OTM options beyond what Black-Scholes predicts. This is part of why the volatility skew exists—the market charges extra for OTM options because their volga provides valuable convexity to holders.

    Trading Implications

    For Volatility Sellers

    If you sell OTM options (iron condors, credit spreads), you're short both vanna and volga:

  • Short vanna: IV spikes shift delta against you on both sides of the trade
  • Short volga: Your short options become increasingly sensitive to further IV changes, compounding your losses during a volatility event

    • This is why iron condors can lose dramatically during market stress—it's not just gamma. Vanna and volga amplify the damage.

    For Volatility Buyers

    Long straddles, long strangles, and tail-risk hedges benefit from positive vanna and volga:

  • Long vanna: IV expansion shifts deltas in your favor, increasing directional profits
  • Long volga: Your position becomes more sensitive to further IV expansion, creating convex payoffs

    • For Portfolio Hedging

    Understanding vanna helps you hedge more accurately. A simple delta hedge doesn't account for how your delta will shift when IV changes. If you're hedging a portfolio during a potential VIX spike, you need to over-hedge because vanna will increase your effective delta as IV rises.

    Should Retail Traders Care?

    Most retail traders don't need to calculate vanna and volga. But understanding them qualitatively explains behavior you'll encounter:

  • Why OTM options sometimes move more than delta alone would predict during volatile sessions
  • Why iron condors can lose three months of profits in a single day during a VIX spike
  • Why deep OTM protective puts are priced higher than Black-Scholes implies
  • Why options near earnings often behave strangely as IV shifts rapidly

    • OptionsPilot's options data provides the Greeks you need for position management, while understanding second-order Greeks like vanna and volga gives you the conceptual framework to anticipate how your positions will behave during the market's most challenging moments.