Calibration of Derivative Pricing Models: a Multi-Agent Reinforcement Learning Perspective
This addresses the calibration challenge in quantitative finance for practitioners, offering a novel computational approach that is incremental in applying RL to an existing problem.
The paper tackles the problem of calibrating derivative pricing models to market option prices by formulating it as a game and using deep multi-agent reinforcement learning to search for stochastic processes that fit the data, achieving results that learn local volatility and path-dependence to minimize Bermudan option prices.
One of the most fundamental questions in quantitative finance is the existence of continuous-time diffusion models that fit market prices of a given set of options. Traditionally, one employs a mix of intuition, theoretical and empirical analysis to find models that achieve exact or approximate fits. Our contribution is to show how a suitable game theoretical formulation of this problem can help solve this question by leveraging existing developments in modern deep multi-agent reinforcement learning to search in the space of stochastic processes. Our experiments show that we are able to learn local volatility, as well as path-dependence required in the volatility process to minimize the price of a Bermudan option. Our algorithm can be seen as a particle method \textit{à la} Guyon \textit{et} Henry-Labordere where particles, instead of being designed to ensure $σ_{loc}(t,S_t)^2 = \mathbb{E}[σ_t^2|S_t]$, are learning RL-driven agents cooperating towards more general calibration targets.