Variational Autoencoders in Volatility and Option Pricing

The Black–Scholes–Merton model is a groundbreaking and foundational framework in option pricing; however, it has well-known limitations. Several extensions have been developed to address these issues, including stochastic volatility and Lévy process-based models, which are largely parametric.

Reference [1] proposes a semi-parametric approach to overcome these limitations. Specifically, the model consists of three components:

1. Variational Autoencoder (VAE) to generate return distributions, capturing non-normal features such as skewness and fat tails, using a tail-weighted loss to better represent extreme events and generate realistic synthetic return paths,
2. An implied volatility model based on LightGBM, which predicts volatility using option characteristics and market sentiment, capturing the volatility surface more effectively than constant volatility assumptions, and
3. Pricing framework using Multi-Level Monte Carlo, which simulates paths based on VAE-generated returns and predicted volatility, achieving similar accuracy with lower computational cost than standard Monte Carlo methods.

The authors pointed out,

A VAE model was trained on historical log-returns of the NIFTY50 index to learn a latent representation of returns. This approach allowed us to capture complex, non-Gaussian structures in the return distribution and to generate synthetic return paths that reflect both normal and extreme market behavior. A quantile-based sampling strategy was adopted during data splitting to ensure the preservation of rare tail events in both training and validation sets. This made the model more resilient to imbalanced data and improved its ability to learn representative latent dynamics. Additionally, to estimate implied volatility, we utilized a LightGBM regression model trained on a diverse set of features, including option-specific variables such as strike price, moneyness, time to expiry and market-level sentiment indicators. The synthetic samples generated by the VAE were then used as inputs to a two-level MLMC simulation framework to estimate option prices more efficiently than conventional Monte Carlo methods. The MLMC approach reduced computational time significantly, while maintaining high fidelity in price estimation.

Empirical evaluation of our full pricing framework demonstrated that the proposed pipeline outperformed the classical Black-Scholes model across a wide range of market conditions. This improvement was consistent across both call and put options, as well as for different moneyness criteria. In particular, the model showed a clear edge in scenarios involving longer time to expiry.

In short, VAE was trained to capture non-Gaussian features and generate realistic synthetic return paths. Implied volatility was estimated using a LightGBM model with option features and sentiment inputs, and the resulting outputs were fed into a two-level MLMC framework for efficient option pricing. The approach reduced computational cost while maintaining accuracy and consistently outperformed the BSM model across market conditions, particularly for longer maturities.

This contribution is valuable and can be extended in several directions, for example, by applying the Variational Autoencoder framework to stress testing. However, the approach has limitations, including the lack of enforcement of no-arbitrage conditions.

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

References

[1] Sapna, S., & Mohan, B. R. (2026). Variational autoencoders for option pricing: A semi-parametric approach to eliminating traditional assumptions. Expert Systems With Applications, 321, 132216.

Post Source Here: Variational Autoencoders in Volatility and Option Pricing

source https://harbourfronts.com/variational-autoencoders-volatility-option-pricing/