Deep Hedging

Deeper Hedging: A New Agent-based Model for Effective Deep Hedging ArXiv ID: 2310.18755 “View on arXiv” Authors: Unknown Abstract We propose the Chiarella-Heston model, a new agent-based model for improving the effectiveness of deep hedging strategies. This model includes momentum traders, fundamental traders, and volatility traders. The volatility traders participate in the market by innovatively following a Heston-style volatility signal. The proposed model generalises both the extended Chiarella model and the Heston stochastic volatility model, and is calibrated to reproduce as many empirical stylized facts as possible. According to the stylised facts distance metric, the proposed model is able to reproduce more realistic financial time series than three baseline models: the extended Chiarella model, the Heston model, and the Geometric Brownian Motion. The proposed model is further validated by the Generalized Subtracted L-divergence metric. With the proposed Chiarella-Heston model, we generate a training dataset to train a deep hedging agent for optimal hedging strategies under various transaction cost levels. The deep hedging agent employs the Deep Deterministic Policy Gradient algorithm and is trained to maximize profits and minimize risks. Our testing results reveal that the deep hedging agent, trained with data generated by our proposed model, outperforms the baseline in most transaction cost levels. Furthermore, the testing process, which is conducted using empirical data, demonstrates the effective performance of the trained deep hedging agent in a realistic trading environment. ...

Adversarial Deep Hedging: Learning to Hedge without Price Process Modeling ArXiv ID: 2307.13217 “View on arXiv” Authors: Unknown Abstract Deep hedging is a deep-learning-based framework for derivative hedging in incomplete markets. The advantage of deep hedging lies in its ability to handle various realistic market conditions, such as market frictions, which are challenging to address within the traditional mathematical finance framework. Since deep hedging relies on market simulation, the underlying asset price process model is crucial. However, existing literature on deep hedging often relies on traditional mathematical finance models, e.g., Brownian motion and stochastic volatility models, and discovering effective underlying asset models for deep hedging learning has been a challenge. In this study, we propose a new framework called adversarial deep hedging, inspired by adversarial learning. In this framework, a hedger and a generator, which respectively model the underlying asset process and the underlying asset process, are trained in an adversarial manner. The proposed method enables to learn a robust hedger without explicitly modeling the underlying asset process. Through numerical experiments, we demonstrate that our proposed method achieves competitive performance to models that assume explicit underlying asset processes across various real market data. ...

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. ...

Efficient Learning of Nested Deep Hedging using Multiple Options ArXiv ID: 2305.12264 “View on arXiv” Authors: Unknown Abstract Deep hedging is a framework for hedging derivatives in the presence of market frictions. In this study, we focus on the problem of hedging a given target option by using multiple options. To extend the deep hedging framework to this setting, the options used as hedging instruments also have to be priced during training. While one might use classical pricing model such as the Black-Scholes formula, ignoring frictions can offer arbitrage opportunities which are undesirable for deep hedging learning. The goal of this study is to develop a nested deep hedging method. That is, we develop a fully-deep approach of deep hedging in which the hedging instruments are also priced by deep neural networks that are aware of frictions. However, since the prices of hedging instruments have to be calculated under many different conditions, the entire learning process can be computationally intractable. To overcome this problem, we propose an efficient learning method for nested deep hedging. Our method consists of three techniques to circumvent computational intractability, each of which reduces redundant computations during training. We show through experiments that the Black-Scholes pricing of hedge instruments can admit significant arbitrage opportunities, which are not observed when the pricing is performed by deep hedging. We also demonstrate that our proposed method successfully reduces the hedging risks compared to a baseline method that does not use options as hedging instruments. ...