A deep learning approach to data-driven model-free pricing and to martingale optimal transport

Neufeld, Ariel; Sester, Julian

doi:10.48550/arxiv.2103.11435

Cited by 3 publications

(3 citation statements)

References 36 publications

(73 reference statements)

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“…We refer to [9], [20] [32], or [35], which are excellent monographs on neural networks, for a general introduction to networks, as well as to [7], [12], [18], [24], [25], [26], [43], [46], [51] for applications in financial mathematics.…”

Section: Setting and Main Resultsmentioning

confidence: 99%

Detecting data-driven robust statistical arbitrage strategies with deep neural networks

Neufeld¹,

Sester²,

Yin³

2022

Preprint

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We present an approach, based on deep neural networks, that allows identifying robust statistical arbitrage strategies in financial markets. Robust statistical arbitrage strategies refer to self-financing trading strategies that enable profitable trading under model ambiguity. The presented novel methodology does not suffer from the curse of dimensionality nor does it depend on the identification of cointegrated pairs of assets and is therefore applicable even on high-dimensional financial markets or in markets where classical pairs trading approaches fail. Moreover, we provide a method to build an ambiguity set of admissible probability measures that can be derived from observed market data. Thus, the approach can be considered as being model-free and entirely datadriven. We showcase the applicability of our method by providing empirical investigations with highly profitable trading performances even in 50 dimensions, during financial crises, and when the cointegration relationship between asset pairs stops to persist.

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Section: Setting and Main Resultsmentioning

confidence: 99%

Detecting data-driven robust statistical arbitrage strategies with deep neural networks

Neufeld¹,

Sester²,

Yin³

2022

Preprint

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“…Further, our paper contributes to the recent literature on deep learning approaches in hedging, starting from the seminal work Buehler et al (2019) and followed by Gümbel and Schmidt (2020), Cuchiero et al (2020), Cao et al (2021), Carbonneau (2021), Carbonneau and Godin (2021), Chen and Wan (2021), Horváth et al (2021), Neufeld and Sester (2021a), amongst many others (see also Ruf and Wang (2020) for a review).…”

Section: Introductionmentioning

confidence: 94%

Robust deep hedging

Lütkebohmert¹,

Schmidt²,

Sester³

2021

Preprint

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We study pricing and hedging under parameter uncertainty for a class of Markov processes which we call generalized affine processes and which includes the Black-Scholes model as well as the constant elasticity of variance (CEV) model as special cases. Based on a general dynamic programming principle, we are able to link the associated nonlinear expectation to a variational form of the Kolmogorov equation which opens the door for fast numerical pricing in the robust framework.The main novelty of the paper is that we propose a deep hedging approach which efficiently solves the hedging problem under parameter uncertainty. We numerically evaluate this method on simulated and real data and show that the robust deep hedging outperforms existing hedging approaches, in particular in highly volatile periods.

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“…Since the ambiguity set in the two-stage DRO problem we are considering is only constrained by the fixed marginals, its inner maximization problem corresponds to a multi-marginal optimal transport problem, with the cost function being the optimal value of the second-stage decision problem. Most numerical methods for multi-marginal optimal transport and related problems with non-discrete marginals rely on discretization (see, e.g., (Carlier, Oberman, and Oudet 2015, Eckstein, Guo, Lim, and Ob lój 2021, Guo and Ob lój 2019, Neufeld and Sester 2021a) and/or regularization techniques (see, e.g., (Cohen, Arbel, and Deisenroth 2020, De Gennaro Aquino and Bernard 2020, De Gennaro Aquino and Eckstein 2020, Eckstein and Kupper 2019, Eckstein, Kupper, and Pohl 2020, Henry-Labordère 2019, Neufeld and Sester 2021b) and do not provide computable estimates of approximation errors. Recently, developed a numerical method that is capable of computing feasible and approximately optimal solutions of high-dimensional multi-marginal optimal transport problems.…”

Section: Literature Reviewmentioning

confidence: 99%

Numerical method for approximately optimal solutions of two-stage distributionally robust optimization with marginal constraints

Neufeld¹,

Xiang²

2022

Preprint

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We consider a general class of two-stage distributionally robust optimization (DRO) problems which includes prominent instances such as task scheduling, the assemble-to-order system, and supply chain network design.The ambiguity set is constrained by fixed marginal distributions that are not necessarily discrete. We develop a numerical algorithm for computing approximately optimal solutions of such problems. Through replacing the marginal constraints by a finite collection of linear constraints, we derive a relaxation of the DRO problem which serves as its upper bound. We can control the relaxation error to be arbitrarily close to 0. We develop duality results and transform the inf-sup problem into an inf-inf problem. This leads to a numerical algorithm for two-stage DRO problems with marginal constraints which solves a linear semiinfinite optimization problem. Besides an approximately optimal solution, the algorithm computes both an upper bound and a lower bound for the optimal value of the problem. The difference between the computed bounds provides a direct sub-optimality estimate of the computed solution. Most importantly, one can choose the inputs of the algorithm such that the sub-optimality is controlled to be arbitrarily small. In our numerical examples, we apply the proposed algorithm to task scheduling, the assemble-to-order system, and supply chain network design. The ambiguity sets in these problems involve a large number of marginals, which include both discrete and continuous distributions. The numerical results showcase that the proposed algorithm computes high-quality robust decisions along with their corresponding sub-optimality estimates with practically reasonable magnitudes that are not over-conservative.

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A deep learning approach to data-driven model-free pricing and to martingale optimal transport

Cited by 3 publications

References 36 publications

Detecting data-driven robust statistical arbitrage strategies with deep neural networks

Detecting data-driven robust statistical arbitrage strategies with deep neural networks

Robust deep hedging

Numerical method for approximately optimal solutions of two-stage distributionally robust optimization with marginal constraints

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