Artikel

Interval estimation of value-at-risk based on nonparametric models

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.

Language
Englisch

Bibliographic citation
Journal: Econometrics ; ISSN: 2225-1146 ; Volume: 6 ; Year: 2018 ; Issue: 4 ; Pages: 1-30 ; Basel: MDPI

Classification
Wirtschaft
Subject
risk measures
quantile estimation
financial time series
Value-at-Risk
choquet integral
possibility theory
maxitive kernel
kernel estimation
parametric models

Event
Geistige Schöpfung
(who)
Khraibani, Hussein
Nehme, Bilal
Strauss, Olivier
Event
Veröffentlichung
(who)
MDPI
(where)
Basel
(when)
2018

DOI
doi:10.3390/econometrics6040047
Handle
Last update
10.03.2025, 11:44 AM CET

Data provider

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Object type

  • Artikel

Associated

  • Khraibani, Hussein
  • Nehme, Bilal
  • Strauss, Olivier
  • MDPI

Time of origin

  • 2018

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