How do you construct a volatility surface?
A volatility surface is a three-dimensional plot that shows how implied volatility varies with both strike price and time to maturity for a given underlying asset. Commonly used in options pricing and risk management.
At first glance, constructing a volatility surface seems to be a straightforward exercise!
Identify options that trade on the assets or securities of interest, obtain prices for those options across strikes and expirations, and compute implied vols from those prices.
The implied volatility is the volatility value that makes the theoretical price of an option equal to its market price.
Different options contracts with the same underlying asset may have different implied volatilities. Even if they have the same strike price and expiration date. This is because implied volatility reflects the market’s expectation of future price movements of the underlying asset.
The volatility surface is constructed by organizing implied volatility values into a matrix with strike prices on one axis and maturities on the other. The matrix then becomes smoothed and interpolated to create a continuous surface that can become plotted in three dimensions.
The resulting volatility surface can be used to analyze and price options on the underlying asset. By visualizing the surface, traders and analysts can identify patterns in implied volatility that may reflect market expectations of future price movements. This information can become used to develop trading strategies, assess risk, and make informed investment decisions.
Overall, the volatility surface provides a useful tool for understanding the complex relationship between option prices, implied volatility, and market expectations.
Constructing a volatility surface involves collecting market data, calculating implied volatility, organizing the data into a matrix. Furthermore, interpolating the data to create a smooth surface, and visualizing the surface using a plotting tool.
Sebastian Jaimungal, a professor at the University of Toronto recently published research to; “introduce a new approach for generating sequences of implied volatility (IV) surfaces across multiple assets that is faithful to historical prices.”
Professor Jaimungal and authors look to; “a combination of functional data analysis and neural stochastic differential equations (SDEs) combined with a probability integral transform penalty to reduce model misspecification.” In addition they, “demonstrate that learning the joint dynamics of IV surfaces and prices produces market scenarios that are consistent with historical features and lie within the sub-manifold of surfaces that are free of static arbitrage.”
Read the full paper:
Top 10 Machine Learning Minds on Wall Street 2022
How do you construct a volatility surface?
