This paper derives conditions for the existence of fourth moments of multivariate GARCH processes in the general vector specification and gives explicit results for the fourth moments and autocovariances of the squares and cross-products. Results are provided for the kurtosis and co-kurtosis...

By extending the GARCH option pricing model of Duan (1995) to more flexible volatility es- timation it is shown that the prices of out-of-the-money options strongly depend on volatility features such as asymmetry. Results are provided for the properties of the stationary pricing distribution in...

This paper considers the impact of ordinary least squares (OLS) detrending and the first difference (FD) detrending on autocorrelation estimation in the presence of long memory and deterministic trends. We show that the FD detrending results in inconsistent autocorrelation estimates when the...

In the empirical analysis of financial time series, multivariate GARCH models have been used in various forms. As it is typical for nonlinear models there is yet no unique framework available to uncover dynamic covariance relationships for vector return processes. We introduce a new concept of...

The prices of wine is a key topic for market participants interested in valuing their stock, including dealers, restaurants or consumers who may be interested in optimizing their purchases. As a closely related issue, re-valuation is the need to regularly update the value of a stock. This need...

The EGARCH is a popular model for discrete time volatility since it allows for asymmetric effects and naturally ensures positivity even when including exogenous variables. Estimation and inference is usually done via maximum likelihood. Although some progress has been made recently, a complete...

The main purpose of this handbook is to illustrate the mathematically fundamental implementation of various volatility models in the banking and financial industries, both at home and abroad, through use of real-world, time-sensitive applications. Conceived and written by over two-dozen experts...