Discovering parametrizations of implied volatility with symbolic regression

TL;DR

This paper uses symbolic regression to discover simple, accurate parametric formulas for implied volatility surfaces directly from market data, offering an alternative to traditional models like SVI.

Contribution

It introduces a data-driven method to find analytic implied volatility parametrizations without predefined forms, enhancing flexibility and interpretability.

Findings

Symbolic regression can identify compact implied volatility formulas.

Discovered formulas achieve competitive accuracy with SVI.

The approach offers a flexible alternative to traditional parametrizations.

Abstract

We investigate the data-driven discovery of parametric representations for implied volatility slices. Using symbolic regression, we search for simple analytic formulas that approximate the total implied variance as a function of log-moneyness and maturity. Our approach generates candidate parametrizations directly from market data without imposing a predefined functional form. We compare the resulting formulas with the widely used SVI parametrization in terms of accuracy and simplicity. Numerical experiments indicate that symbolic regression can identify compact parametrizations with competitive fitting performance.