Stochastic Policy Gradient Methods in the Uncertain Volatility Model
A backward actor-critic stochastic policy-gradient scheme is proposed, combining discrete dynamic programming with PPO and one-hidden-layer neural-network approximations of value function and control policy. Continuous controls are represented by a squashed Gaussian policy built on a C-vine correlation-matrix representation that enforces positive definiteness by construction. Beyond robust prices, the trained critic's spatial gradient approximates the superhedging strategy, a
01 ABSTRACT
The paper addresses robust option pricing under joint volatility and correlation uncertainty in the multidimensional Uncertain Volatility Model, where the associated stochastic control problem is high-dimensional and numerically challenging. It proposes a backward actor-critic stochastic policy-gradient scheme whose key ingredient is a squashed Gaussian policy based on a C-vine representation of correlation matrices, ensuring positive definiteness by construction. Numerical experiments on multidimensional derivatives show accurate prices, computational efficiency, and favorable comparison with existing Monte Carlo and machine-learning benchmarks for robust pricing in the Uncertain Volatility Model.
02 KEY FINDINGS
- A backward actor-critic stochastic policy-gradient scheme integrating discrete dynamic programming with Proximal Policy Optimization.
- Continuous controls are parameterized through a squashed Gaussian policy built on a C-vine representation of correlation matrices, enforcing positive definiteness by construction.
- The spatial gradient of the trained critic approximates the superhedging strategy, with quality assessed by a dual formulation that also yields a numerical dual price estimate.
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