A calibrated scenario generation model for heavy-tailed risk factors

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.