Stochastic Policy Gradient Methods in the Uncertain Volatility Model

TL;DR

This paper introduces a novel stochastic policy gradient method using neural networks and a specialized Gaussian policy for robust multidimensional option pricing under uncertainty.

Contribution

It develops a backward actor-critic scheme with a C-vine based Gaussian policy to efficiently solve high-dimensional robust option pricing problems.

Findings

Accurately prices multidimensional derivatives under volatility uncertainty.

Remains computationally efficient compared to existing methods.

Outperforms Monte Carlo and machine-learning benchmarks in robustness.

Abstract

The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control problem is high-dimensional. We propose a backward actor-critic stochastic policy gradient scheme tailored to this setting. The method combines a discrete dynamic programming principle with Proximal Policy Optimization and shallow neural-network approximations of both the value function and the control policy. A key ingredient is the policy parameterization: continuous controls are represented through a squashed Gaussian policy built on a C-vine representation of correlation matrices, which enforces positive semidefiniteness by construction. Numerical experiments on a range of multidimensional derivatives show that the method yields accurate prices, remains computationally efficient, and compares favorably with existing Monte Carlo and machine-learning-based benchmarks for robust pricing in the Uncertain Volatility Model.