Risk-Neutral Generative Networks

Paper: arXiv 2405.17770

Authors: Zhonghao Xian, Xing Yan, Cheuk Hang Leung, Qi Wu

Abstract

We present a functional generative approach to extract risk-neutral densities from market prices of options. Specifically, we model the log-returns on the time-to-maturity continuum as a stochastic curve driven by standard normal. We then use neural nets to represent the term structures of the location, the scale, and the higher-order moments, and impose stringent conditions on the learning process to ensure the neural net-based curve representation is free of static arbitrage. This specification is structurally clear in that it separates the modeling of randomness from the modeling of the term structures of the parameters. It is data adaptive in that we use neural nets to represent the shape of the stochastic curve. It is also generative in that the functional form of the stochastic curve, although parameterized by neural nets, is an explicit and deterministic function of the standard normal. This explicitness allows for the efficient generation of samples to price options across strikes and maturities, without compromising data adaptability. We have validated the effectiveness of this approach by benchmarking it against a comprehensive set of baseline models. Experiments show that the extracted risk-neutral densities accommodate a diverse range of shapes. Its accuracy significantly outperforms the extensive set of baseline models–including three parametric models and nine stochastic process models–in terms of accuracy and stability. The success of this approach is attributed to its capacity to offer flexible term structures for risk-neutral skewness and kurtosis.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an innovative functional generative approach (RNGN) to extract risk-neutral densities while strictly adhering to static no-arbitrage constraints. Its empirical evaluation is exceptionally rigorous, benchmarking performance against twelve parametric and stochastic baseline models across multiple asset regimes. The combination of structural neural network parametrization and probabilistic foundations delivers a compelling blend of mathematical soundness and practical accuracy.

Research Flowchart

  flowchart TD
    A[Goal: Extract Arbitrage-Free Risk-Neutral Densities from Option Prices] --> B[Input: Market Option Prices across Strikes and Maturities]
    B --> C[Model Modeling: Represent Stochastic Curve via Standard Normal & Neural Networks]
    C --> D[Neural Networks: Parameterize Term Structures of Location, Scale, Skewness & Kurtosis]
    D --> E[Optimization: Impose Static Arbitrage Constraints during Learning]
    E --> F[Validation: Benchmark against 12 Baseline Models]
    F --> G[Outcomes: Superior Accuracy, Stability, & Flexible Skewness/Kurtosis Shapes]

Cited References (127)

1. Neural networks for portfolio analysis with cardinality constraints (2023)
2. Entropic dynamic time warping kernels for co-evolving financial time series analysis (2020)
3. Uncertainty-aware portfolio management with risk-sensitive multiagent network (2022)
4. Neural networks for portfolio analysis in high-frequency trading (2023)
5. A Continuous Volatility Forecasting Model Based on Neural Differential Equations and Scale-Similarity (2024)
6. Generative adversarial nets (2014)
7. The range of traded option prices (2007)
8. Arbitrage-free market models for option prices: The multi-strike case (2008)

0 of 127 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.