Paper: arXiv 2605.06670

Authors: Lokman A Abbas-Turki, Jean-François Chassagneux, Jean-Philippe Lemor, Grégoire Loeper, Simon Sananes

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper addresses a challenging high-dimensional stochastic control problem in robust option pricing using advanced reinforcement learning techniques. It integrates sophisticated mathematical parameterizations, such as C-vine decompositions for correlation matrices, with strong numerical experiments comparing favorably to existing benchmarks.

Research Flowchart

  flowchart TD
    A[Goal: Solve High-Dimensional Robust Option Pricing under Uncertain Volatility & Correlation] --> B[Inputs: Multidimensional Derivatives & Volatility/Correlation Uncertainty Ranges]
    B --> C[Framework: Backward Dynamic Programming + Actor-Critic RL]
    C --> D[Methodology: Squashed Gaussian Policy via C-Vine Matrix Representation & PPO]
    D --> E[Neural Networks: Shallow NN Approximations for Value Function & Control Policy]
    E --> F[Outcomes: Accurate Robust Prices & Efficient Scaling vs. MC/ML Benchmarks]

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2 of 58 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.