# Volatility Surface

> The volatility surface maps implied volatility across every strike and expiry. Learn how it is built, what its shape says, how it is used and how it changes.

Source: https://learn.tradelabsai.com/volatility/volatility-surface/  
Track: Volatility · Level: Advanced · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "Volatility Surface", https://learn.tradelabsai.com/volatility/volatility-surface/

The volatility surface is a three dimensional picture of implied volatility for one underlying: strike (or moneyness) along one axis, time to expiry along another, and implied volatility as the height. Each slice at a fixed expiry is a smile or skew; each slice at a fixed strike is a term structure. Option traders, risk managers and pricing models all rely on the surface, because it summarises how the market prices every option on that underlying at once.

## The two slices

| Slice | Shows | Lesson |
|---|---|---|
| Across strikes at one expiry | Smile or skew | [Volatility Smile and Skew](https://learn.tradelabsai.com/volatility/volatility-smile-and-skew/) |
| Across expiries at one strike or moneyness | Term structure | [Volatility Term Structure](https://learn.tradelabsai.com/volatility/volatility-term-structure/) |

## A sample equity index surface

| Expiry | 90% strike | 95% | 100% (ATM) | 105% | 110% |
|---|---|---|---|---|---|
| 1 month | 24.0% | 19.5% | 15.5% | 13.0% | 12.5% |
| 3 months | 22.0% | 19.0% | 16.5% | 14.5% | 13.5% |
| 1 year | 21.0% | 19.5% | 18.0% | 16.5% | 15.5% |

Illustrative figures. Typical features:

- **Skew is steepest at short expiries** and flattens with time.
- **At the money volatility rises with expiry** in calm markets (upward term structure).
- **Long dated volatility is more stable** than short dated.

## How a surface is built

1. **Collect option quotes** across strikes and expiries; use mid prices and remove stale or illiquid quotes.
2. **Compute implied volatility** for each option using a suitable model (Black Scholes, Black 76, or a tree for American options).
3. **Use out of the money options** on each side, since they are usually more liquid and less affected by dividends and early exercise.
4. **Fit a smooth model** to each expiry, such as SVI or SABR.
5. **Interpolate across time,** usually in total variance.
6. **Check for arbitrage:** no negative butterfly prices and no falling total variance across expiries.

See [Volatility Interpolation and Extrapolation](https://learn.tradelabsai.com/options/volatility-interpolation/).

## What the surface is used for

- **Pricing any option,** including strikes and expiries that are not quoted.
- **Marking portfolios** to market consistently.
- **Risk management:** measuring exposure to shifts, tilts and twists of the surface.
- **Exotic pricing:** local volatility models are calibrated directly to the surface. See [Local Volatility](https://learn.tradelabsai.com/options/local-volatility/).
- **Relative value:** finding options that look expensive or cheap compared with neighbours.

## Ways the surface moves

| Movement | Description | Typical cause |
|---|---|---|
| Parallel shift | All volatilities rise or fall together | Change in overall market fear |
| Term structure twist | Short dated moves more than long dated | Event or shock |
| Skew steepening | Put volatilities rise relative to calls | Selloff, demand for protection |
| Smile curvature change | Wings rise or fall relative to at the money | Changing tail risk pricing |

**Example: A selloff on the surface**
An index falls 4% in a day. One month at the money volatility jumps from 15.5% to 22%, while one year volatility rises only from 18% to 20%. The term structure inverts in the short end. One month 90% strike puts rise from 24% to 30%. A trader short one month puts loses on both the price move and the volatility jump; a trader long one year volatility gains, but less. See [Volatility Surface Dynamics](https://learn.tradelabsai.com/volatility/volatility-surface-dynamics/).

## Vega by bucket

Because different parts of the surface move differently, traders measure vega for each expiry and strike bucket, not just in total. A book can be vega flat overall while being long short dated volatility and short long dated volatility, a position that can still lose money if the term structure twists. See [Managing Portfolio Greeks](https://learn.tradelabsai.com/options/managing-portfolio-greeks/).

## Surfaces in other markets

- **FX:** quoted in delta terms with at the money, risk reversal and butterfly at each expiry.
- **Interest rates:** a cube of expiry, underlying swap tenor and strike, often called the swaption volatility cube. See [SABR Model](https://learn.tradelabsai.com/options/sabr-model/).
- **Commodities:** each futures contract month has its own smile, linked to its own underlying price.

## Frequently asked questions

### What is a volatility surface?

A map of implied volatility for every strike and expiry of options on one underlying, combining the smile and the term structure.

### Why is the volatility surface important?

It lets traders price any option consistently, measure detailed volatility risk and calibrate models for exotic options.

### How does the volatility surface change in a selloff?

Usually short dated volatility rises most, the term structure inverts and put skew steepens.

Next, look closely at the time dimension in [Volatility Term Structure](https://learn.tradelabsai.com/volatility/volatility-term-structure/).

## Continue learning

- Next lesson: [Volatility Term Structure](https://learn.tradelabsai.com/volatility/volatility-term-structure/)
- Previous lesson: [Volatility Smile and Skew](https://learn.tradelabsai.com/volatility/volatility-smile-and-skew/)
- Related: [Volatility Smile and Skew](https://learn.tradelabsai.com/volatility/volatility-smile-and-skew/): Implied volatility differs by strike, forming a smile or skew. Learn the shapes in equities, FX and commodities, why they exist and how to measure skew.
- Related: [Volatility Term Structure](https://learn.tradelabsai.com/volatility/volatility-term-structure/): The volatility term structure plots implied volatility across expiries. Learn what upward and inverted curves mean, how events show up and how traders use it.
- Related: [Volatility Interpolation and Extrapolation](https://learn.tradelabsai.com/options/volatility-interpolation/): Volatility interpolation fills gaps between quoted options to build a smooth, arbitrage free surface. Learn the main methods, SVI and the arbitrage checks.
- Related: [Local Volatility](https://learn.tradelabsai.com/options/local-volatility/): The local volatility model, from Dupire and Derman Kani, makes volatility depend on price and time so it fits every listed option. Learn how it works and its limits.
- Related: [Volatility Surface Dynamics](https://learn.tradelabsai.com/volatility/volatility-surface-dynamics/): Surface dynamics describe how implied volatilities change when the underlying moves. Learn sticky strike, sticky delta and why hedges depend on them.