What is a Volatility Surface?

Every option listed on a stock has a market price. A pricing model such as Black–Scholes turns a volatility into a price. Run the model backward, and the price gives back a volatility: the option's implied volatility, the volatility the market is pricing in.

Do this for every strike price \(K\) and every expiration \(T\), and you get a function of two variables:

\(\sigma_{\mathrm{imp}}(K,\ T)\)

Plot it in three dimensions, and you have the volatility surface.

If the assumptions of Black–Scholes held exactly, the surface would be flat: one stock, one volatility. Real surfaces are never flat. Their shape shows what the market fears, and when.
A carved wooden relief model of a curved surface on a cartographer's desk, lit by an oil lamp

Remember

Four things to keep in mind about the volatility surface.

  • Implied volatility is read from prices, not forecast: it is the volatility that makes a model's price match the market's.

  • Real surfaces are never flat. A flat surface is what Black–Scholes assumes, and the market disagrees.

  • Slice across strikes and you get the smile, or skew. Slice across expirations and you get the term structure.

  • Watch the shape, not just the level: a steeper skew or an inverted term structure says more than a higher average.

Why the Surface Isn't Flat

Black–Scholes assumes one constant volatility and share prices whose log-returns follow a bell curve. Real markets break both assumptions, and the surface records how.

The skew. For stock and index options, low strikes carry higher implied volatility than high strikes. Investors pay up for puts that protect against a fall, and real returns have fatter tails than the bell curve allows: large drops happen more often than the model expects. Index options have shown this skew ever since the crash of October 1987.

The term structure. Across expirations, implied volatility usually rises gently in calm markets, since the far future holds more room for trouble. In a selloff it inverts: short-dated options become the most expensive, because the danger is now.

Events. A known date, such as an earnings report, adds a bump to every expiration that spans it.

Together, these effects give the surface its shape. Reading that shape is how traders see what the market expects.
3D chart of a volatility surface: implied volatility by strike and months to expiration, with the one-month smile highlighted in coral and the at-the-money term structure in navy

Three Shapes You Will See on a Real Surface

  • The Skew

    A stock trades at $100. Its one-month put with a $90 strike might be priced at 28% implied volatility, while the $100 option is priced at 21%. Investors pay extra for protection against a fall.

  • The Earnings Bump

    Options that expire just after an earnings report carry higher implied volatility than those that expire just before it. Once the news is out, that extra volatility drains away overnight: traders call it volatility crush.

  • The Inverted Term Structure

    In a selloff, one-month options might trade at 40% implied volatility while one-year options stay near 25%. The fear is about the near term, so the term structure slopes down instead of up.

FAQ

  • What is the difference between historical and implied volatility?

    Historical volatility is measured from past share prices: how much the stock actually moved. Implied volatility is read from option prices today: how much movement the market is paying for. The first looks back; the second is the market's price for what lies ahead.

  • What is the difference between a volatility smile and a volatility skew?

    Both describe how implied volatility changes across strikes at one expiration. A smile rises on both sides of the at-the-money strike, as is common in currency options. A skew rises mostly on one side: for stocks and stock indexes, low strikes carry the higher implied volatility.

  • Why do out-of-the-money puts have higher implied volatility?

    Investors who own stock buy puts as insurance against a fall, and that demand raises their price. Large drops also happen more often than the bell curve behind Black–Scholes predicts. A higher price, run back through the model, shows up as a higher implied volatility.

  • What is volatility crush?

    Before a scheduled event such as an earnings report, implied volatility rises, because a big move might be coming. Once the news is out, the uncertainty is gone and implied volatility falls sharply, often overnight. An option can lose value even when the stock moves the way its buyer hoped.

  • How is the VIX related to the volatility surface?

    The VIX condenses part of one surface into a single number. It is computed from the prices of S&P 500 index options across many strikes, and states the implied volatility of the index over the next 30 days. The full surface shows far more: every strike, and every expiration.

Learn Volatility, the Greeks, and the Strategies Built on Them

Our Stock Options course covers implied volatility and volatility surfaces, the VIX, and calculating volatility in Google Sheets, along with the Greeks, covered calls, spreads, straddles and strangles, in video lessons with quizzes.