A New Approach to Backtesting and Risk Model Selection

43 Pages Posted: 17 Jun 2016 Last revised: 14 Oct 2018

See all articles by Jacopo Corbetta

Jacopo Corbetta

Ecole des Ponts ParisTech

Ilaria Peri

University of London - Economics, Mathematics and Statistics

Date Written: September 17, 2018


Backtesting risk measures represents a challenge and complex methods are often required. In this paper, we propose a new framework for backtesting that can be applied to every law invariant risk measures. We base our approach on the formalization of the concept of level of coverage associated with the risk model as defined in the original Basel Accord. Thus, we propose two simple hypothesis tests based only on results of probability theory without requiring any approximation or simulation. In addition, within this new framework, we introduce a methodology for selecting the best performing risk model among all the existing alternatives. This proposal adds value to the current state of the art, since, using the traditional loss function approach, any comparison among forecasting outcomes of different risk models appeared to be meaningless. A series of simulation studies show that our hypothesis tests provide similar size and power to the classical binomial tests of value at risk and well-known tests of expected shortfall. A final experiment on real data allows determining the best risk measure procedures among the value at risk, expected shortfall, expectiles and lambda value at risk in different time windows over more than 40 years of daily data.

Keywords: backtesting, capital requirement, hypothesis test, risk measures, model selection

JEL Classification: C12, C52, C53, G32

Suggested Citation

Corbetta, Jacopo and Peri, Ilaria, A New Approach to Backtesting and Risk Model Selection (September 17, 2018). Available at SSRN: https://ssrn.com/abstract=2796253 or http://dx.doi.org/10.2139/ssrn.2796253

Jacopo Corbetta

Ecole des Ponts ParisTech ( email )

6-8 avenue Blaise-Pascal, Cité Descartes
Marne-la-Vallée Cedex 2, 77455

Ilaria Peri (Contact Author)

University of London - Economics, Mathematics and Statistics ( email )

United States

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