Calibration of Derivative Pricing Models: a Multi-Agent Reinforcement Learning Perspective

Abstract

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{\`{a} la} Guyon \textit{et} Henry-Labordere where particles, instead of being designed to ensure $\sigma_{loc}(t,S_t)^2 = \mathbb{E}[\sigma_t^2|S_t]$, are learning RL-driven agents cooperating towards more general calibration targets.