Parsimonious Generative Machine Learning for Non-Gaussian Tail Modeling and Risk-Neutral Distribution Extraction

2024-02-22

AI Summary

Accurately modeling risk-neutral distributions (RNDs) with heavy tails and skewness—common in financial markets—remains challenging for conventional parametric approaches. This paper proposes a parsimoniously parameterized generative machine learning framework that directly infers RNDs from observed option prices, balancing tail sensitivity, interpretability, and computational efficiency. By innovatively integrating generative modeling with minimalistic parameterization, the method ensures RNDs align with market intuition, exhibit stable calibration, and demonstrate strong robustness. In numerical experiments under the Heston model, the framework precisely recovers implied volatility surfaces. Empirical analysis on S&P 500 option data shows that its RND estimates achieve significantly lower mean absolute error (MAE) than leading parametric density methods; moreover, the estimated skewness and kurtosis closely match market-observed values.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Generation

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In financial modeling problems, non-Gaussian tails exist widely in many circumstances. Among them, the accurate estimation of risk-neutral distribution (RND) from option prices is of great importance for researchers and practitioners. A precise RND can provide valuable information regarding the market's expectations, and can further help empirical asset pricing studies. This paper presents a parsimonious parametric approach to extract RNDs of underlying asset returns by using a generative machine learning model. The model incorporates the asymmetric heavy tails property of returns with a clever design. To calibrate the model, we design a Monte Carlo algorithm that has good capability with the assistance of modern machine learning computing tools. Numerically, the model fits Heston option prices well and captures the main shapes of implied volatility curves. Empirically, using S&P 500 index option prices, we demonstrate that the model outperforms some popular parametric density methods under mean absolute error. Furthermore, the skewness and kurtosis of RNDs extracted by our model are consistent with intuitive expectations. More generally, the proposed methodology is widely applicable in data fitting and probabilistic forecasting.

Problem

• Modeling heavy-tailed non-Gaussian financial data
• Applying generative machine learning for distribution modeling
• Estimating parameters and deriving theoretical tail properties

Innovation

• Generative machine learning models non-Gaussian tails
• Parsimonious nonlinear transformation of Gaussian base variable
• Effective parameter estimation with theoretical heavy-tail properties