Deep Hedging with Minimal Near-Martingale Measures under Trading Frictions

Summary

This work uses machine learning to find minimal equivalent martingale measures for simulated markets containing tradable instruments, such as a spot asset and options on that asset. It extends the approach to markets with trading frictions by seeking near-martingale measures: under these measures, hedging-instrument prices behave as martingales within their bid–ask spreads. Removing drift in this way aims to separate hedging from opportunities a strategy might otherwise exploit for statistical arbitrage.

The resulting measures are used to train Deep Hedging for exotic payoffs, with the aim of producing a hedge that reflects the payoff and market frictions rather than simulator drift. The authors discuss the hedge’s robustness to errors in the original market simulator and describe applications to two simulators. The supplied summary does not specify the simulator designs, quantitative results, or conditions under which the robustness holds, so it does not establish universal performance across markets.

Key ideas

• Machine learning is used to estimate minimal equivalent martingale measures for simulated markets.
• With trading frictions, the method seeks measures under which prices remain martingales within bid–ask spreads.
• Removing drift aims to prevent the learned hedge from exploiting statistical arbitrage in the simulator.
• The approach applies Deep Hedging to exotic payoffs using the adjusted market measure.
• The authors discuss robustness to simulator estimation error and applications to two market simulators.

Tags

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


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









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.

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