In this paper we examine the usefulness of multivariate semi-parametric GARCH models for portfolio selection under a Value-at-Risk (VaR) constraint. First, we specify and estimate several alternative multivariate GARCH models for daily returns on the S&P 500 and Nasdaq indexes. Examining the within sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly ...

the research problem investigated in this paper is modeling volatility and analyzing risk and return’s relationship in tehran stock exchange using garch-family models including garch(1,1), garch(2,2), egarch(1,1), pgarch(1,1), tgarch(1,1), garch(1,1)-m and cgarch(1,1). using the daily returns of tehran stock exchange companies, we focused on two portfolios of all the companies during a 10-year-...

A new variant of the ARCH class of models for forecasting conditional variance, to be called the Generalized AutoRegressive Conditional Heteroskedasticity Parkinson Range (GARCH-PARK-R) Model, is proposed. The GARCH-PARK-R model, utilizing the extreme values, is a good alternative to the Realized Volatility that requires a large amount of intra-daily data, which remain relatively costly and are...

We use a discrete time analysis, giving necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH concept to continuous time processes. Our “COGARCH” (continuous time GARCH) model, based on a single background driving Lévy process, is different from, though related to, other continuous time stochast...

It is well known that as the time interval between two consecutive observations shrinks to zero, a properly constructed GARCH model will weakly converge to a bivariate diffusion. Naturally the European option price under the GARCH model will also converge to its bivariate diffusion counterpart. This paper investigates the convergence speed of the GARCH option price. We show that the European op...

We develop univariate regime-switching GARCH (RS-GARCH) models wherein the conditional variance switches in time from one GARCH process to another. The switching is governed by a time-varying probability, specified as a function of past information. We provide sufficient conditions for geometric ergodicity and existence of moments. Because of path dependence, maximum likelihood estimation is no...

Conditions for the existence of strictly stationary multivariate GARCH processes in the so-called BEKK parametrisation, which is the most general form of multivariate GARCH processes typically used in applications, and for their geometric ergodicity are obtained. The conditions are that the driving noise is absolutely continuous with respect to the Lebesgue measure and zero is in the interior o...

We revisit the risk-return relation using the component GARCH model and international daily MSCI stock market data. In contrast with the previous evidence obtained from weekly and monthly data, daily data show that the relation is positive in almost all markets and often statistically significant. Likelihood ratio tests reject the standard GARCH model in favor of the component GARCH model, whic...

Most existing econometric models such as ARCH(q) and GARCH(p,q) take into account heteroskedasticity (non-stationarity) of time series. However, the original ARCH(q) and GARCH(p,q) models do not take into account the asymmetry of the market’s response to positive and to negative changes. Several heuristic modifications of ARCH(q) and GARCH(p,q) models have been proposed that take this asymmetry...