Market Frictions

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. ...

A Game of Competition for Risk ArXiv ID: 2305.18941 “View on arXiv” Authors: Unknown Abstract In this study, we present models where participants strategically select their risk levels and earn corresponding rewards, mirroring real-world competition across various sectors. Our analysis starts with a normal form game involving two players in a continuous action space, confirming the existence and uniqueness of a Nash equilibrium and providing an analytical solution. We then extend this analysis to multi-player scenarios, introducing a new numerical algorithm for its calculation. A key novelty of our work lies in using regret minimization algorithms to solve continuous games through discretization. This groundbreaking approach enables us to incorporate additional real-world factors like market frictions and risk correlations among firms. We also experimentally validate that the Nash equilibrium in our model also serves as a correlated equilibrium. Our findings illuminate how market frictions and risk correlations affect strategic risk-taking. We also explore how policy measures can impact risk-taking and its associated rewards, with our model providing broader applicability than the Diamond-Dybvig framework. We make our methodology and open-source code available at https://github.com/louisabraham/cfrgame Finally, we contribute methodologically by advocating the use of algorithms in economics, shifting focus from finite games to games with continuous action sets. Our study provides a solid framework for analyzing strategic interactions in continuous action games, emphasizing the importance of market frictions, risk correlations, and policy measures in strategic risk-taking dynamics. ...

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. ...