Deep Hedging: Learning Risk-Neutral Implied Volatility Dynamics

Abstract

This paper is an earlier draft of our work on removing the drift published in Risk.
See also the arxiv version Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures


Abstract

We present a numerically efficient approach for machine-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, for example as discussed in our recent work here;

2) Find a risk-neutral density, specifically in our approach 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.

Keywords: Stochastic Implied Volatility, Deep Hedging, Minimal Entropy Martingale Measure, Statistical Arbitrage, Machine Learning, Deep Learning, Reinforcement Learning

JEL Classification: C15, C45, C5, C53, C6, C63, G0