Discovering parametrizations of implied volatility with symbolic regression

Paper: arXiv 2603.21892

Authors: Martin Keller-Ressel, Hannes Nikulski

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.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents an innovative application of symbolic regression to discover closed-form implied volatility parametrizations directly from market data. While the mathematical foundations rely primarily on genetic programming and existing volatility geometry rather than deep proofs, the methodology is novel and offers a strong data-driven alternative to heuristic models like SVI.

Research Flowchart

  flowchart TD
    A[Research Goal: Discover data-driven implied volatility parametrizations] --> B[Input Data: Option market data log-moneyness & maturity]
    B --> C[Methodology: Symbolic Regression vs SVI Baseline]
    C --> D[Computational Process: Search functional space for total implied variance formulas]
    D --> E[Outcome: Compact, simple analytic formulas without predefined forms]
    E --> F[Key Finding: Discovered models achieve competitive fit vs SVI]