Estimating Value-at-Risk and Expected Shortfall: Do Polynomial Expansions Outperform Parametric Densities?

Brenda Castillo-Brais, Ángel León and Juan Mora ()
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Brenda Castillo-Brais: Departamento de Fundamentos del Análisis Económico, Campus San Vicente del Raspeig, Universidad de Alicante, 03690 Alicante, Spain
Ángel León: Departamento de Fundamentos del Análisis Económico, Campus San Vicente del Raspeig, Universidad de Alicante, 03690 Alicante, Spain
Juan Mora: Departamento de Fundamentos del Análisis Económico, Campus San Vicente del Raspeig, Universidad de Alicante, 03690 Alicante, Spain

Mathematics, 2022, vol. 10, issue 22, 1-17

Abstract: We assess Value-at-Risk (VaR) and Expected Shortfall (ES) estimates assuming different models for the standardized returns: distributions based on polynomial expansions such as Cornish-Fisher and Gram-Charlier, and well-known parametric densities such as normal, skewed-t and Johnson. This paper aims to analyze whether models based on polynomial expansions outperform the parametric ones. We carry out the model performance comparison in two stages: first, with a backtesting analysis of VaR and ES; and second, using loss functions. Our backtesting results show that all distributions, except for normal ones, perform quite well in VaR and ES estimations. Regarding the loss function analysis, we conclude that polynomial expansions (specifically, the Cornish-Fisher one) usually outperform parametric densities in VaR estimation, but the latter (specifically, the Johnson density) slightly outperform the former in ES estimation; however, the gains of using one approach or the other are modest.

Keywords: value-at-risk; expected shortfall; polynomial expansions; backtesting (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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