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Preprints, Working Papers, ... Year : 2023

Learning out-of-sample Expected Shortfall and Conditional Tail Moments with neural networks. Application to cryptocurrency data

Abstract

We propose new parameterizations for neural networks in order to estimate out-of-sample Expected Shortfall, and even more generally, out-of-sample conditional tail moments, in heavy-tailed settings as functions of confidence levels. The proposed neural network estimator is able to extrapolate in the distribution tails thanks to an extension of the usual extreme-value second-order condition to an arbitrary order. The convergence rate of the uniform error between the log-conditional tail moment and its neural network approximation is established. The finite sample performance of the neural network estimator is compared to bias-reduced extreme-value competitors on simulated data. It is shown that our method outperforms them in difficult heavy-tailed situations where other estimators almost all fail. Finally, the neural network estimator is tested on real data to investigate the behavior of cryptocurrency extreme loss returns.
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Dates and versions

hal-04347859 , version 1 (15-12-2023)
hal-04347859 , version 2 (06-03-2024)
hal-04347859 , version 3 (14-03-2024)

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  • HAL Id : hal-04347859 , version 3

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Michaël Allouche, Stéphane Girard, Emmanuel Gobet. Learning out-of-sample Expected Shortfall and Conditional Tail Moments with neural networks. Application to cryptocurrency data. 2023. ⟨hal-04347859v3⟩
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