Discovering parametrizations of implied volatility with symbolic regression

Battle Count: 96

Highly relevant to quantitative trading, particularly in options market making and volatility trading. Implied volatility surface construction is a core task for market makers. The paper demonstrates that data-driven methods can discover competitive parametrizations without human-imposed functional forms, potentially uncovering new structures in volatility data. The SVI parametrization is industry-standard, and finding alternatives with better accuracy-complexity tradeoffs directly impacts pricing, hedging, and risk management. However, the practical adoption would require rigorous no-arbitrage guarantees and integration into existing trading infrastructure.

Moderate complexity. PySR is an accessible open-source Python package with good documentation. The core symbolic regression is straightforward to set up. However, the domain-specific aspects add complexity: structuring IV data into slices, implementing Lee's tail bound penalties, k-means clustering for computational tractability, conditional parametric regression with per-slice parameter optimization, and monitoring Durrleman's condition. The evolutionary search is stochastic and requires multiple runs. Understanding the financial context (no-arbitrage constraints, SVI parametrization) is essential for meaningful application.

PySR is open-source and well-documented. The methodology is clearly described with specific settings (basis functions, templates, clustering parameters). However, the primary data set D1 (SPX IV data from IVolatility.com) is commercial and not freely available. The curated data set D2 is extracted from VolaDynamics website using WebPlotDigitizer. Multiple runs with different random initializations yield different results, making exact reproduction difficult. No code repository is explicitly provided.