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On time-scaling of risk and the square–root–of–time rule

Danielsson, Jon and Zigrand, Jean-Pierre (2003) On time-scaling of risk and the square–root–of–time rule. Discussion paper, 439. Financial Markets Group, London School of Economics and Political Science, London, UK.

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Abstract

Many financial applications, such as risk analysis and derivatives pricing, depend on time scaling of risk. A common method for this purpose, though only correct when returns are iid normal, is the square–root–of–time rule where an estimated quantile of a return distribution is scaled to a lower frequency by the square-root of the time horizon. The aim of this paper is to examine time scaling of risk when returns follow a jump diffusion process. It is argued that a jump diffusion is well-suited for the modeling of systemic risk, which is the raison d’etre of the Basel capital adequacy proposals. We demonstrate that the square–root–of–time rule leads to a systematic underestimation of risk, whereby the degree of underestimation worsens with the time horizon, the jump intensity and the confidence level. As a result, even if the square–root–of–time rule has widespread applications in the Basel Accords, it fails to address the objective of the Accords.

Item Type: Monograph (Discussion Paper)
Official URL: http://fmg.lse.ac.uk
Additional Information: © 2003 The Authors
Library of Congress subject classification: H Social Sciences > HG Finance
H Social Sciences > HB Economic Theory
Journal of Economic Literature Classification System: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty
G - Financial Economics > G1 - General Financial Markets > G18 - Government Policy and Regulation
G - Financial Economics > G2 - Financial Institutions and Services > G20 - General
Sets: Research centres and groups > Financial Markets Group (FMG)
Collections > Economists Online
Collections > LSE Financial Markets Group (FMG) Working Papers
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: 439
Date Deposited: 12 Aug 2009 09:58
URL: http://eprints.lse.ac.uk/24827/

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