Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures

TL;DR

This paper introduces a machine learning method to identify minimal equivalent martingale measures in markets with frictions, enabling the creation of robust, drift-free hedging strategies for exotic payoffs.

Contribution

It extends deep hedging techniques to markets with frictions by finding near-martingale measures, improving hedge robustness and removing arbitrage influences.

Findings

Successfully finds near-martingale measures in markets with frictions.

Demonstrates improved hedge robustness against market estimation errors.

Applies method to two different market simulators.

Abstract

We present a machine learning approach for finding minimal equivalent martingale measures for markets simulators of tradable instruments, e.g. for a spot price and options written on the same underlying. We extend our results to markets with frictions, in which case we find "near-martingale measures" under which the prices of hedging instruments are martingales within their bid/ask spread. By removing the drift, we are then able to learn using Deep Hedging a "clean" hedge for an exotic payoff which is not polluted by the trading strategy trying to make money from statistical arbitrage opportunities. We correspondingly highlight the robustness of this hedge vs estimation error of the original market simulator. We discuss applications to two market simulators.