Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures
This addresses hedging robustness for financial traders in markets with frictions, though it appears incremental as it extends existing methods to handle frictions.
The paper tackles the problem of hedging exotic payoffs in markets with frictions by removing drift from market simulators using minimal equivalent near-martingale measures, resulting in a robust hedge that is not polluted by statistical arbitrage opportunities.
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.