Deep Hedging: Learning Risk-Neutral Implied Volatility Dynamics
This work addresses the challenge of modeling financial derivatives pricing under realistic market frictions for quantitative finance practitioners.
The paper tackles the problem of learning risk-neutral implied volatility dynamics under transaction costs and trading constraints by developing a numerically efficient approach that trains a market simulator and finds the minimal entropy martingale measure. The resulting model enables risk-neutral pricing and Deep Hedging applications.
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.