A Comparison of Reinforcement Learning and Deep Trajectory Based Stochastic Control Agents for Stepwise Mean-Variance Hedging

TL;DR

This paper compares reinforcement learning and deep trajectory-based stochastic control for stepwise mean-variance hedging of European call options, highlighting their performance, strengths, and limitations in a simulated Black-Scholes environment.

Contribution

It provides a detailed comparative analysis of RL and stochastic control approaches for hedging, offering insights and blueprints for developing autonomous hedging agents.

Findings

RL and stochastic control achieve comparable hedging performance.

The study identifies strengths and limitations of each approach.

Provides a framework for future autonomous hedging agent development.

Abstract

We consider two data-driven approaches to hedging, Reinforcement Learning and Deep Trajectory-based Stochastic Optimal Control, under a stepwise mean-variance objective. We compare their performance for a European call option in the presence of transaction costs under discrete trading schedules. We do this for a setting where stock prices follow Black-Scholes-Merton dynamics and the "book-keeping" price for the option is given by the Black-Scholes-Merton model with the same parameters. This simulated data setting provides a "sanitized" lab environment with simple enough features where we can conduct a detailed study of strengths, features, issues, and limitations of these two approaches. However, the formulation is model free and could allow any other setting with available book-keeping prices. We consider this study as a first step to develop, test, and validate autonomous hedging agents, and we provide blueprints for such efforts that address various concerns and requirements.