Derivative Hedging

Experimental Analysis of Deep Hedging Using Artificial Market Simulations for Underlying Asset Simulators ArXiv ID: 2404.09462 “View on arXiv” Authors: Unknown Abstract Derivative hedging and pricing are important and continuously studied topics in financial markets. Recently, deep hedging has been proposed as a promising approach that uses deep learning to approximate the optimal hedging strategy and can handle incomplete markets. However, deep hedging usually requires underlying asset simulations, and it is challenging to select the best model for such simulations. This study proposes a new approach using artificial market simulations for underlying asset simulations in deep hedging. Artificial market simulations can replicate the stylized facts of financial markets, and they seem to be a promising approach for deep hedging. We investigate the effectiveness of the proposed approach by comparing its results with those of the traditional approach, which uses mathematical finance models such as Brownian motion and Heston models for underlying asset simulations. The results show that the proposed approach can achieve almost the same level of performance as the traditional approach without mathematical finance models. Finally, we also reveal that the proposed approach has some limitations in terms of performance under certain conditions. ...

Quantum Risk Analysis of Financial Derivatives ArXiv ID: 2404.10088 “View on arXiv” Authors: Unknown Abstract We introduce two quantum algorithms to compute the Value at Risk (VaR) and Conditional Value at Risk (CVaR) of financial derivatives using quantum computers: the first by applying existing ideas from quantum risk analysis to derivative pricing, and the second based on a novel approach using Quantum Signal Processing (QSP). Previous work in the literature has shown that quantum advantage is possible in the context of individual derivative pricing and that advantage can be leveraged in a straightforward manner in the estimation of the VaR and CVaR. The algorithms we introduce in this work aim to provide an additional advantage by encoding the derivative price over multiple market scenarios in superposition and computing the desired values by applying appropriate transformations to the quantum system. We perform complexity and error analysis of both algorithms, and show that while the two algorithms have the same asymptotic scaling the QSP-based approach requires significantly fewer quantum resources for the same target accuracy. Additionally, by numerically simulating both quantum and classical VaR algorithms, we demonstrate that the quantum algorithm can extract additional advantage from a quantum computer compared to individual derivative pricing. Specifically, we show that under certain conditions VaR estimation can lower the latest published estimates of the logical clock rate required for quantum advantage in derivative pricing by up to $\sim 30$x. In light of these results, we are encouraged that our formulation of derivative pricing in the QSP framework may be further leveraged for quantum advantage in other relevant financial applications, and that quantum computers could be harnessed more efficiently by considering problems in the financial sector at a higher level. ...

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. ...