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

Danielsson, Jon ORCID: 0009-0006-9844-7960 and Zigrand, Jean-Pierre ORCID: 0000-0002-7784-4231 (2003) On time-scaling of risk and the square–root–of–time rule. Financial Markets Group Discussion Papers (439). Financial Markets Group, The 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.ac.uk
Additional Information:	© 2003 The Authors
Divisions:	Financial Markets Group
Subjects:	H Social Sciences > HG Finance H Social Sciences > HB Economic Theory
JEL classification:	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
Date Deposited:	12 Aug 2009 09:58
Last Modified:	01 Oct 2024 04:03
URI:	http://eprints.lse.ac.uk/id/eprint/24827

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