Risk-Neutral Generative Networks

TL;DR

This paper introduces a neural network-based generative model for option pricing and risk-neutral density extraction, ensuring no arbitrage and outperforming existing models in accuracy and stability.

Contribution

It presents a novel neural generative approach that models risk-neutral densities with flexible term structures, improving accuracy over traditional methods.

Findings

Outperforms baseline models in accuracy and stability

Effectively captures diverse risk-neutral density shapes

Ensures no arbitrage in the learning process

Abstract

We present a generative approach to price options and extract risk-neutral densities from the market. Specifically, we model the underlying log-returns on the time-to-maturity continuum as a generative model from standard normal. Neural nets are used to represent the term structures of the location, the scale, and the higher-order moments. We impose stringent conditions on the learning process to ensure no arbitrage. This model allows for the efficient generation of samples to price options across strikes and maturities. 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.