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.
翻译:我们提出一种机器学习方法,为可交易工具的市场模拟器寻找最低等效的马丁格措施,例如现货价格和根据同一基本条件拟定的选择方案。我们把结果推广到摩擦市场,在这种情况下,我们发现“近婚措施”,套期保值工具的价格在其出价/风险扩散范围内是马丁格。通过去除漂移,我们就能学到如何用深套套套用“清洁”的对冲来换取一种外来的回报,这种回报不受贸易战略试图从统计套利机会中赚钱的污染。我们相应地强调了这种对冲相对于原始市场模拟器估计错误的稳健性。我们讨论了对两个市场模拟器的应用。