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.

Autorentext
Wenbo Hu is a director of quantitative trading at Bell Trading in Chicago. Dr. Hu obtained a master of financial mathematics from Peking University in 2001 and a PhD in Financial Mathematics from Florida State University in 2005. Since then, he has been working for Bell Trading to develop futures and options black box trading system.

Klappentext
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.