Volatility Surface Modelling

Fitting a volatility surface involves using mathematical models to interpolate and extrapolate implied volatilities. The goal is to create a continuous surface that best fits the observed market data points.

An implied volatility surface is a 3-D plot that plots volatility smile and term structure of volatility in a consolidated three-dimensional surface for all options on a given underlying asset.

One of the most powerful tools to capture this behavior is the volatility surface — a three-dimensional view of how implied volatility behaves across different strike prices and maturities.

What is the volatility surface? Volatility surface is the term options traders use to describe the volatility of all options across all strikes and all expirations for a single symbol.

The volatility surface evolved from the concept of the volatility smile, which plots implied volatility against strike prices for a single expiration date. This gives a 2D visual.

The volatility surface is a three-dimensional chart that shows how implied volatility varies across different strike prices and expiration dates for options on the same stock.

The Volatility Surface allows one to execute historical analysis of implied volatility (thus option price level), i.e. to compare the current option price with the price of the option with the same moneyness and days remaining until expiration, which was