Improved risk estimation in multifractal records: Application to the value at risk in finance

Mikhail I. Bogachev and Armin Bunde
Phys. Rev. E 80, 026131 – Published 31 August 2009

Abstract

We suggest a risk estimation method for financial records that is based on the statistics of return intervals between events above/below a certain threshold Q and is particularly suited for multifractal records. The method is based on the knowledge of the probability WQ(t;Δt) that within the next Δt units of time at least one event above Q occurs, if the last event occurred t time units ago. We propose an analytical estimate of WQ and show explicitly that the proposed method is superior to the conventional precursory pattern recognition technique widely used in signal analysis, which requires considerable fine tuning and is difficult to implement. We also show that the estimation of the Value at Risk, which is a standard tool in finances, can be improved considerably by the method.

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  • Received 16 July 2008

DOI:https://doi.org/10.1103/PhysRevE.80.026131

©2009 American Physical Society

Authors & Affiliations

Mikhail I. Bogachev and Armin Bunde

  • Institut für Theoretische Physik III, Justus-Liebig-Universität Giessen, 35392 Giessen, Germany

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Issue

Vol. 80, Iss. 2 — August 2009

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