Robust Hedging GANs: Towards Automated Robustification of Hedging Strategies

Abstract

The availability of deep hedging has opened new horizons for solving hedging problems under a large variety of realistic market conditions. At the same time, any model–be it a traditional stochastic model or a market generator–is at best an approximation of market reality, prone to model-misspecification and estimation errors. This raises the question, how to address the risk of discrepancy between anticipated distribution and market reality, in an automated way. This paper presents a natural extension of the original deep hedging framework to address uncertainty in the data generating process via an adversarial approach inspired by GANs. This is achieved through an interplay of three modular components: (i) a (deep) hedging engine, (ii) a data-generating process (that is model agnostic permitting a large variety of classical models as well as machine learning-based market generators), and (iii) a notion of distance on model space to measure deviations between our market prognosis and reality. We do not restrict the ambiguity set to a region around a reference model, but instead penalize deviations from the anticipated distribution. We demonstrate this in numerical experiments to benchmark our framework against other existing results.