Variational Autoencoders for Arbitrage-Free Volatility Modeling

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Machine learning and AI are transforming investing by enabling data-driven decision-making, uncovering hidden patterns, and automating complex strategies. From algorithmic trading and portfolio optimization to risk management and sentiment analysis, AI-driven models process vast amounts of data with speed and precision, identifying opportunities that traditional methods might miss.

Most ML and AI approaches have been applied to building predictive models. Reference [1], however, suggests using ML techniques in risk management. Specifically, it explores the use of Variational Autoencoders for generating synthetic volatility surfaces for stress testing and scenario analysis.

The paper develops a robust synthetic data generation framework using parameterized Heston models. It implements comprehensive arbitrage validation, ensuring critical no-arbitrage conditions, including calendar spread and butterfly arbitrage constraints, are preserved. The authors pointed out,

First, we have demonstrated that synthetic data generation using carefully parameterized Heston models can effectively overcome the traditional barriers of limited market data in illiquid markets. By generating over 13,500 synthetic surfaces—compared to the typical constraint of fewer than 100 market-observable surfaces, we have significantly enhanced the robustness and reliability of our VAE training process. Our methodology succeeds in preserving critical no-arbitrage conditions, specifically, both calendar spread and butterfly arbitrage constraints validate its practical applicability in real-world trading environments. .. A key innovation of our approach is expanding the idea of latent space optimization which was alluded to by Bergeron et al [2] and its independence from historical market data for training purposes. This characteristic makes our framework particularly valuable for emerging markets, newly introduced derivatives, and other scenarios where historical data is scarce or non-existent. The ability to generate realistic, arbitrage-free synthetic surfaces provides practitioners with a powerful tool for price simulation and risk assessment in illiquid markets…The successful reconstruction of surfaces with significant missing data points (demonstrated through our test case with 100 randomly removed points) showcases the model’s robustness and practical utility. Extending the framework to examine the model’s performance under various market stress scenarios could constitute further research directions.

This is a significant contribution to the advancement of ML and AI in finance, particularly in risk management—an area with much yet to be explored.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Nteumagne,  B. F.; Donfack,  H. A.; Wafo Soh,  C. Variational Autoencoders for Completing the Volatility Surfaces. Preprints 2025, 2025021482. https://doi.org/10.20944/preprints202502.1482.v1

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