Applied Quantitative Finance by Wolfgang Karl Hardle

Part I
Market Risk

Chapter 1
VaR in High Dimensional Systems-A
Conditional Correlation Approach
H. Herwartz, B. Pedrinha and F.H.C. Raters
Abstract In empirical finance, multivariate volatility models are widely used to
capture both volatility clustering and contemporaneous correlation of asset return
vectors. In higher dimensional systems, parametric specifications often become
intractable for empirical analysis owing to large parameter spaces. On the contrary,
feasible specifications impose strong restrictions that may not be met by financial
data as, for instance, constant conditional correlation (CCC). Recently, dynamic
conditional correlation (DCC) models have been introduced as a means to solve the
trade off between model feasibility and flexibility. Here, we employ alternatively
the CCC and the DCC modeling framework to evaluate the Value-at-Risk associated
with portfolios comprising major U.S. stocks. In addition, we compare their perfor-

mances with corresponding results obtained from modeling portfolio returns directly
via univariate volatility models.

Applied Quantitative Finance by Wolfgang Karl Hardle