Model-Free Deep Hedging with Transaction Costs and Light Data Requirements

TL;DR

This paper demonstrates that a neural network can be effectively trained with very few data trajectories to outperform classical option hedging models, even with transaction costs, making deep hedging more practical.

Contribution

It introduces a model-free deep hedging approach that requires significantly fewer data trajectories, enhancing practicality over previous methods.

Findings

Neural networks trained with only 256 trajectories outperform classical models.

The approach is effective within the Geometric Brownian Motion framework.

It simplifies deep hedging implementation for real-time financial data.

Abstract

Option pricing theory, such as the Black and Scholes (1973) model, provides an explicit solution to construct a strategy that perfectly hedges an option in a continuous-time setting. In practice, however, trading occurs in discrete time and often involves transaction costs, making the direct application of continuous-time solutions potentially suboptimal. Previous studies, such as those by Buehler et al. (2018), Buehler et al. (2019) and Cao et al. (2019), have shown that deep learning or reinforcement learning can be used to derive better hedging strategies than those based on continuous-time models. However, these approaches typically rely on a large number of trajectories (of the order of $10^5$ or $10^6$) to train the model. In this work, we show that using as few as 256 trajectories is sufficient to train a neural network that significantly outperforms, in the Geometric Brownian Motion framework, both the classical Black & Scholes formula and the Leland model, which is arguably one of the most effective explicit alternatives for incorporating transaction costs. The ability to train neural networks with such a small number of trajectories suggests the potential for more practical and simple implementation on real-time financial series.