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Directional entropy and tail uncertainty, with applications to financial hazard

Directional entropy and tail uncertainty, with applications to financial hazard “Mine is a long and sad tale”, said the Mouse, turning to Alice and sighing. “It is a long tail certainly,” said Alice, looking down with wonder at the Mouse's tail; “but why do you call it sad?” And she kept on puzzling about it while the mouse was speaking … Financial risk management metrics such as value at risk (VaR) can be illuminated by means of a regime-specific concept of directional entropy. This enables a change of measure via a rescaling function to an equivalent logistic distribution, one that has the same total and directional entropies at the chosen critical point. VaR rescaling adjusts the critical probability to capture the long tail entropy. The scaling function can be used as a comparative metric for tail length, or equivalent conditional value at risk, even where moments do not exist. Directional entropy can also be used to identify regions of maximal exposure to new information, which can actually increase entropy rather than collapse it. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantitative Finance Taylor & Francis

Directional entropy and tail uncertainty, with applications to financial hazard

Quantitative Finance , Volume 11 (3): 10 – Mar 1, 2011
10 pages

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References (29)

Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1469-7696
eISSN
1469-7688
DOI
10.1080/14697681003685548
Publisher site
See Article on Publisher Site

Abstract

“Mine is a long and sad tale”, said the Mouse, turning to Alice and sighing. “It is a long tail certainly,” said Alice, looking down with wonder at the Mouse's tail; “but why do you call it sad?” And she kept on puzzling about it while the mouse was speaking … Financial risk management metrics such as value at risk (VaR) can be illuminated by means of a regime-specific concept of directional entropy. This enables a change of measure via a rescaling function to an equivalent logistic distribution, one that has the same total and directional entropies at the chosen critical point. VaR rescaling adjusts the critical probability to capture the long tail entropy. The scaling function can be used as a comparative metric for tail length, or equivalent conditional value at risk, even where moments do not exist. Directional entropy can also be used to identify regions of maximal exposure to new information, which can actually increase entropy rather than collapse it.

Journal

Quantitative FinanceTaylor & Francis

Published: Mar 1, 2011

Keywords: Alternative investments; Applied finance; Applied mathematical finance; Applied investment analysis; Asset liability modelling; Asset allocation; Asset management; Asset pricing

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