On time-scaling of risk and the square-root-of-time rule
AbstractMany financial applications, such as risk analysis and derivatives pricing, depend on time scaling of risk.ï¿½ 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.ï¿½ 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Banking & Finance.
Volume (Year): 30 (2006)
Issue (Month): 10 (October)
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- Jean-Pierre Zigrand & Jon Danielsson, 2003. "On time-scaling of risk and the square–root–of–time rule," FMG Discussion Papers dp439, Financial Markets Group.
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