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IMA Journal of Management Mathematics Advance Access published online on February 1, 2006
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpi044
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© The authors 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received October 3, 2003
Revised October 5, 2005
Accepted November 18, 2005

Article

A calibrated scenario generation model for heavy-tailed risk factors

Qi-Man Shao 1, Hao Wang 2 *, and Hao Yu 3

1 Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong and University of Oregon, Eugene, OR 97403, USA
2 Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
3 Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada

* To whom correspondence should be addressed.
Hao Wang, E-mail: haowang{at}uoregon.edu


  Abstract

In this paper, a calibrated scenario generation model for multivariate risk factors with heavy-tailed distributions is developed. This model includes the standard and classical model of scenario generation developed by J. P. Morgan as a special case. A rotation method is introduced to preserve the correlation information between risk factors, and a mixture of normal distributions is used to model and fit each marginal heavy-tailed distribution. Based on the scenario generation, a non-parametric method is applied to estimate the extreme value-at-risk and value-at-risk confidence interval of a portfolio with heavy-tailed distribution.

Keywords: VaR; VaR CI; heavy tails; non-parametric method; Monte Carlo simulation; scenario generation.
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