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Interval Estimation of Value-at-Risk Based on Nonparametric Models

Hussein Khraibani (), Bilal Nehme () and Olivier Strauss ()
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Hussein Khraibani: Department of Applied Mathematics, Faculty of Sciences, Lebanese University, Beirut 2038 1003, Lebanon
Bilal Nehme: Department of Economics, Faculty of Economic Sciences & Business Administration, Lebanese University, Beirut 2038 1003, Lebanon
Olivier Strauss: Department of Robotics, LIRMM University of Montpellier II, 61 rue Ada, 34392 Montpellier CEDEX 5, France

Econometrics, 2018, vol. 6, issue 4, 1-30

Abstract: Value-at-Risk (VaR) has become the most important benchmark for measuring risk in portfolios of different types of financial instruments. However, as reported by many authors, estimating VaR is subject to a high level of uncertainty. One of the sources of uncertainty stems from the dependence of the VaR estimation on the choice of the computation method. As we show in our experiment, the lower the number of samples, the higher this dependence. In this paper, we propose a new nonparametric approach called maxitive kernel estimation of the VaR. This estimation is based on a coherent extension of the kernel-based estimation of the cumulative distribution function to convex sets of kernel. We thus obtain a convex set of VaR estimates gathering all the conventional estimates based on a kernel belonging to the above considered convex set. We illustrate this method in an empirical application to daily stock returns. We compare the approach we propose to other parametric and nonparametric approaches. In our experiment, we show that the interval-valued estimate of the VaR we obtain is likely to lead to more careful decision, i.e., decisions that cannot be biased by an arbitrary choice of the computation method. In fact, the imprecision of the obtained interval-valued estimate is likely to be representative of the uncertainty in VaR estimate.

Keywords: risk measures; quantile estimation; financial time series; Value-at-Risk; choquet integral; possibility theory; maxitive kernel; kernel estimation; parametric models (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2018
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