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

  • Jean-Pierre Zigrand

    ()

  • Jon Danielsson

    ()

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.

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Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp439.

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Date of creation: Mar 2003
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Handle: RePEc:fmg:fmgdps:dp439
Contact details of provider: Web page: http://www.lse.ac.uk/fmg/

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