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

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 a la Guyon et HenryLabordere where particles, instead of being designed to ensure sigma(loc) (t, S-t)(2) = E[sigma(2)(t) |S-t], are learning RL-driven agents cooperating towards more general calibration targets.