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.� 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Financial Markets Group in its series FMG Discussion Papers with number dp439.
Date of creation: Mar 2003
Date of revision:
Contact details of provider:
Web page: http://www2.lse.ac.uk/fmg/
Other versions of this item:
- Danielsson, Jon & Zigrand, Jean-Pierre, 2006. "On time-scaling of risk and the square-root-of-time rule," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2701-2713, October.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Peter Carr & Liuren Wu, 2003.
"What Type of Process Underlies Options? A Simple Robust Test,"
Journal of Finance,
American Finance Association, vol. 58(6), pages 2581-2610, December.
- Peter Carr & Liuren Wu, 2002. "What Type of Process Underlies Options? A Simple Robust Test," Finance 0207019, EconWPA.
- Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
- Guidolin, Massimo & Timmermann, Allan, 2006.
"Term structure of risk under alternative econometric specifications,"
Journal of Econometrics,
Elsevier, vol. 131(1-2), pages 285-308.
- Massimo Guidolin & Allan Timmerman, 2005. "Term structure of risk under alternative econometric specifications," Working Papers 2005-001, Federal Reserve Bank of St. Louis.
- Guidolin, Massimo & Timmermann, Allan G, 2004. "Term Structure of Risk Under Alternative Econometric Specifications," CEPR Discussion Papers 4645, C.E.P.R. Discussion Papers.
- Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
- Saadi, Samir & Rahman, Abdul, 2008. "Evidence of non-stationary bias in scaling by square root of time: Implications for Value-at-Risk," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(3), pages 272-289, July.
- Gaglianone, Wagner Piazza & Linton, Oliver & Lima, Luiz Renato Regis de Oliveira, 2008.
"Evaluating Value-at-Risk models via Quantile regressions,"
Economics Working Papers (Ensaios Economicos da EPGE)
679, Graduate School of Economics, Getulio Vargas Foundation (Brazil).
- Gaglianone, Wagner Piazza & Lima, Luiz Renato & Linton, Oliver & Smith, Daniel R., 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 150-160.
- Wagner P. Gaglianone & Luiz Renato Lima & Oliver Linton, 2008. "Evaluating Value-at-Risk Models via Quantile Regressions," Working Papers Series 161, Central Bank of Brazil, Research Department.
- Wagner Piazza Gaglianone & Luiz Renato Lima & Oliver Linton & Daniel Smith, 2010. "Evaluating Value-at-Risk Models via Quantile Regression," NCER Working Paper Series 67, National Centre for Econometric Research.
- Gaglianone, Wagner Piazza & Lima, Luiz Renato & Linton, Oliver & Smith, Daniel, . "Evaluating Value-at-Risk models via Quantile Regression," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4883, Universidad Carlos III de Madrid.
- Wagner Piazza Gaglianone & Luiz Renato Lima & Oliver Linton & Daniel Smith, 2009. "Evaluating Value-at-Risk models via Quantile Regression," Economics Working Papers we094625, Universidad Carlos III, Departamento de Economía.
- Santos, André A. P. & Nogales, F. Javier & Ruiz, Esther & Dijk, Dick van, 2012. "Optimal portfolios with minimum capital requirements," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/15745, Universidad Carlos III de Madrid.
- Amadeo Alentorn & Sheri Markose, 2006. "Removing Maturity Effects of Implied Risk Neutral Densities and Related Statistics," Economics Discussion Papers 609, University of Essex, Department of Economics.
- Wang, Jying-Nan & Yeh, Jin-Huei & Cheng, Nick Ying-Pin, 2011. "How accurate is the square-root-of-time rule in scaling tail risk: A global study," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1158-1169, May.
- Alfred Mbairadjim Moussa & Jules Sadefo Kamdem & Arnold F. Shapiro & Michel Terraza, 2012. "Capital asset pricing model with fuzzy returns and hypothesis testing," Working Papers 12-33, LAMETA, Universtiy of Montpellier, revised Sep 2012.
- 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.
- Pérignon, Christophe & Smith, Daniel R., 2010. "Diversification and Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 55-66, January.
- Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
- Guy Kaplanski, Haim Levy, 2010. "The Two-Parameter Long-Horizon Value-at-Risk," Frontiers in Finance and Economics, SKEMA Business School, vol. 7(1), pages 1-20, April.
- Nikolaus Rab & Richard Warnung, 2010. "Scaling portfolio volatility and calculating risk contributions in the presence of serial cross-correlations," Papers 1009.3638, arXiv.org, revised Nov 2011.
- Al Janabi, Mazin A. M., 2009. "Asset Market Liquidity Risk Management: A Generalized Theoretical Modeling Approach for Trading and Fund Management Portfolios," MPRA Paper 19498, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (The FMG Administration).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.