Vega and the Volatility Surface

What a book loses when volatility reprices

Vega is the change in an option’s value for a one point move in implied volatility. Unlike delta it cannot be hedged in the underlying — only with other options — and unlike delta there is no single volatility to hedge against: every strike and every expiry has its own, and the shape they make is the volatility surface. Most of what an options desk argues about is a point on that surface.

Open in the app · Risk & the Greeks · intermediate

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What the lesson covers

1. What it is
2. Where vega lives
3. The surface
4. Second-order vega
5. Risks to watch

Key terms

• Vega — The change in an option’s value for a one point move in implied volatility.
• Implied volatility — The volatility input that makes a model’s price equal the option’s market price.
• Volatility surface — Implied volatility mapped across every strike and every maturity for one underlying.
• Skew — The slope of implied volatility across strikes, quoted in the market as a risk reversal.
• Volga — The sensitivity of vega to volatility itself — the convexity of the volatility exposure.
• Vanna — The cross sensitivity: how vega moves with the underlying, or delta with volatility.

In practice

Volatility is quoted, traded and risk-managed as its own asset on every options desk: the market makes prices in the at-the-money level, the risk reversal and the butterfly rather than in individual option premiums. Variance swaps exist because they give exposure to the whole surface at once without a delta hedging programme attached.

Read next

• Variance Swap — Trade realized volatility directly
• Delta and Gamma — The hedge, and how fast the hedge goes stale
• Cliquet Option — A chain of options, each struck where the last one ended

In the app, Vega and the Volatility Surface carries a five-step lesson, a worked example and a bank of twelve questions drawn differently every sitting.

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Educational content only. Nothing here is financial advice, an offer to trade, or a recommendation to buy or sell any instrument.