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为深度对冲学习风险中性隐含波动率动态

文章 arXiv papers · 作者: Hans Buehler et al.
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总结

文档概述一种数值方法，用于在有限期限内，根据现货和期权价格的模拟路径学习风险中性测度。该设定包含凸交易成本和凸交易约束。学习得到的测度是最小熵鞅测度，通过训练期权价格市场模拟器获得，可用于随机隐含波动率建模、风险中性定价或深度对冲。

论文还刻画了市场动态不存在统计套利的条件：在没有交易成本时，当且仅当动态遵循风险中性测度，该条件才成立。论文进一步描述存在凸成本和交易约束时的情形，将其视为有摩擦环境下资产定价基本定理的对应形式。摘录介绍了该框架，但没有提供数值基准或真实市场数据上的绩效证据。

核心观点

  • 该方法为模拟的现货和期权价格路径学习风险中性测度。
  • 该方法采用两阶段建模方式中的最小熵鞅测度。
  • 所得模型旨在用于有摩擦环境下的风险中性定价和深度对冲。
  • 论文刻画了无成本以及存在凸摩擦和约束时的统计套利条件。
  • 摘录没有提供真实市场绩效基准。

标签

期权波动率机器学习风险管理衍生品定价
全文
# Deep Hedging: Learning Risk-Neutral Implied Volatility Dynamics


# Deep Hedging: Learning Risk-Neutral Implied Volatility Dynamics









We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be used to implement a stochastic implied volatility model in the following two steps: 1. Train a market simulator for option prices, as discussed for example in our recent; 2. Find a risk-neutral density, specifically the minimal entropy martingale measure. The resulting model can be used for risk-neutral pricing, or for Deep Hedging in the case of transaction costs or trading constraints. To motivate the proposed approach, we also show that market dynamics are free from "statistical arbitrage" in the absence of transaction costs if and only if they follow a risk-neutral measure. We additionally provide a more general characterization in the presence of convex transaction costs and trading constraints. These results can be seen as an analogue of the fundamental theorem of asset pricing for statistical arbitrage under trading frictions and are of independent interest.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。