Hedging of Financial Derivative Contracts via Monte Carlo Tree Search

Abstract

The construction of approximate replication strategies for derivative contracts in incomplete markets is a key problem of financial engineering. Recently Reinforcement Learning algorithms for pricing and hedging under realistic market conditions have attracted significant interest. While financial research mostly focused on variations of $Q$-learning, in Artificial Intelligence Monte Carlo Tree Search is the recognized state-of-the-art method for various planning problems, such as the games of Hex, Chess, Go,... This article introduces Monte Carlo Tree Search as a method to solve the stochastic optimal control problem underlying the pricing and hedging of financial derivatives. As compared to $Q$-learning it combines reinforcement learning with tree search techniques. As a consequence Monte Carlo Tree Search has higher sample efficiency, is less prone to over-fitting to specific market models and generally learns stronger policies faster. In our experiments we find that Monte Carlo Tree Search, being the world-champion in games like Chess and Go, is easily capable of directly maximizing the utility of investor's terminal wealth without an intermediate mathematical theory.Comment: Added figures. Added references. Corrected typos. 15 pages, 5 figure