Risk-Neutral Generative Networks

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. © 2026 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.