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

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Author Info
Jean-Pierre Zigrand ()
Jon Danielsson ()

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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.

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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

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  1. Amy S. K. Wong, 2006. "Basel II and the Risk Management of Basket Options with Time-Varying Correlations," International Journal of Central Banking, International Journal of Central Banking, vol. 2(4), December. [Downloadable!]
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