Discovering parametrizations of implied volatility with symbolic regression

2026-03-23

AI Summary

This work proposes a data-driven approach based on symbolic regression to automatically discover concise and highly accurate parametric expressions for the implied volatility surface. The method directly searches market data for analytical forms of total implied variance as a function of log-moneyness and time to maturity, without assuming any predefined functional structure. As the first application of symbolic regression to implied volatility modeling, the resulting formulas are both interpretable and compact, achieving fitting accuracy and model parsimony that rival or even surpass those of the widely used Stochastic Volatility Inspired (SVI) framework.

Technology Category

• Machine Learning: Classification and Regression
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• implied volatility
• symbolic regression
• parametrization
• volatility surface
• data-driven discovery

Innovation

• symbolic regression
• implied volatility
• data-driven discovery
• parametrization
• analytic formulas