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2017 | OriginalPaper | Chapter

Uncertainty in Historical Value-at-Risk: An Alternative Quantile-Based Risk Measure

Authors : Dominique Guégan, Bertrand Hassani, Kehan Li

Published in: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Publisher: Springer International Publishing

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Abstract

The financial industry has extensively used quantile-based risk measures relying on the Value-at-Risk (V aR). They need to be estimated from relevant historical data sets. Consequently, they contain uncertainty due to the finiteness of observations in practice. We propose an alternative quantile-based risk measure (the Spectrum Stress V aR) to capture the uncertainty in the historical V aR approach. This one provides flexibility to the risk manager to implement prudential regulatory framework. It can be a V aR based stressed risk measure. In the end we propose a stress testing application for it.

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Appendix
Available only for authorised users
Footnotes
1
A fat-tailed distribution has the property that exhibits large kurtosis or has power law decay in the tail of the distribution.
 
2
Or if they are not, we assume that we can transform them to an i.i.d set by filtering.
 
3
[x] denotes the largest integer less than or equal to x.
 
4
Asymptotically consistent estimator means \(\boldsymbol{\hat{\theta }}\rightarrow _{(P)}\boldsymbol{\theta }\), where →(P) represents convergence in probability.
 
5
p is the confidence level of historical V aR and q is the confidence level of its confidence interval.
 
6
The data sets are downloaded from Bloomberg.
 
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Metadata
Title
Uncertainty in Historical Value-at-Risk: An Alternative Quantile-Based Risk Measure
Authors
Dominique Guégan
Bertrand Hassani
Kehan Li
Copyright Year
2017
Book
Mathematical and Statistical Methods for Actuarial Sciences and Finance

Print ISBN: 978-3-319-50233-5

Electronic ISBN: 978-3-319-50234-2

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-50234-2_10