Robust Hedging GANs

ArXiv ID: 2307.02310 “View on arXiv”

Authors: Unknown

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 furnish a modelling setup with tools that can address the risk of discrepancy between anticipated distribution and market reality, in an automated way. Automated robustification is currently attracting increased attention in numerous investment problems, but it is a delicate task due to its imminent implications on risk management. Hence, it is beyond doubt that more activity can be anticipated on this topic to converge towards a consensus on best practices. 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 to automate robustification in our hedging objective. 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. Our suggested choice for each component is motivated by model agnosticism, allowing a seamless transition between settings. Since all individual components are already used in practice, we believe that our framework is easily adaptable to existing functional settings.

Keywords: Deep Hedging, Model Misspecification, Generative Adversarial Networks (GANs), Robust Optimization, Market Risk

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics including rough paths, signatures, GANs, and distributionally robust optimization, indicating high mathematical density. It also demonstrates empirical validity through numerical experiments benchmarking against existing results, though the summary suggests a theoretical/preprint focus rather than full backtesting code, placing it at moderate-to-high empirical rigor.

  flowchart TD
    A["Research Goal:<br>Automate robust hedging<br>under model misspecification"] --> B{"Methodology:<br>Adversarial GAN Framework"}
    
    B --> C["Data/Inputs:<br>Market Data &<br>Anticipated Distribution"]
    
    C --> D["Component 1:<br>Deep Hedging Engine<br>Compute optimal hedge"]
    
    D --> E["Component 2:<br>Market Generator<br>Simulates counterfactual scenarios"]
    
    E --> F["Component 3:<br>Distance Metric<br>Measure distribution deviation"]
    
    F --> G{"Adversarial Loop:<br>Min-Max Optimization"}
    
    G --> H["Outcome:<br>Robust Hedging Strategy<br>Resistant to model errors"]