Calibration of Multivariate Generalized Hyperbolic Distributions

The distributions of many financial quantities are§well-known to have heavy tails, exhibit skewness. We §study an especially promising family: multivariate §generalized hyperbolic distributions(GH). This §family includes Gaussian and Student t §distributions, and the so-called skewed t §distributions. We describe a way to stably §calibrate GH distributions for a wider range of§parameters than has previously been reported. §§We apply GH distributions in three financial§applications. First, we forecast the VaR for stock§index returns, and show that the GH distributions§outperform the Gaussian distribution. Second, we§calculate an efficient frontier for equity portfolio§optimization under the skewed-t distribution and we§show that the Gaussian efficient frontier is actually§unreachable. Third, we build an intensity-based model§to price Basket Credit Default Swaps by calibrating§the skewed t distribution directly, without the need§to separately calibrate the skewed t copula.§§This book is useful to academic research of GH§distributions for both theory and calibration. It is§also useful to quantitative finance analysts and§numeric algorithm developers.