Multivariate Volatility Models belong to the class of nonlinear models for financial data. Here we want to focus on multivariate GARCH models. These models assume that the variance of the innovation distribution follows a time dependent process conditional on information which is generated by...

We analyze daily changes of two log foreign exchange (FX) rates involving the Deutsche Mark (DEM) for the period 1975 - 1998, namely FX-rates measured against the US dollar (USD) and the Japanese yen (JPY). Ta account for volatility e1ustering we fit a GARCH(l,l)-model with leptokurtic...

Daily returns of financial assets are frequently found to exhibit positive autocorrelation at lag 1. When specifying a linear AR(l) conditional mean, one may ask how this predictability affects option prices. We investigate the dependence of option prices on autoregressive dynamics under...

Based on daily VDAX data this paper analyzes the factors governing the movements of implied volatilities of options on the German stock index DAX. Using Principal Components Analysis over the sample period from 1996 to 1997, we derive common factors representing "shift" and "curvature" of the...

We establish a relation between stochastic volatility models and the class of generalized hyperbolic distributions. These distributions have been found to fit exceptionally well to the empirical distribution of stock returns. We review the background of hyperbolic distributions and prove...