Mixed Normal Conditional Heteroskedasticity

Abstract

Abstract:Both unconditional mixed-normal distributions and GARCH models with fat-tailed conditional distributions have been employed for modeling financial return data. We consider a mixed-normal distribution coupled with a GARCH-type structure which allows for conditional variance in each of the components as well as dynamic feedback between the components. Special cases and relationships with previously proposed specifications are discussed and stationarity conditions are derived. An empirical application to NASDAQindex data indicates the appropriateness of the model class and illustrates that the approach can generate a plausible disaggregation of the conditional variance process, in which the components' volatility dynamics have a clearly distinct behavior that is, for example, compatible with the well-known leverage effect.JEL Classification: C22, C51, G10

Semiparametric estimation of multi-asset portfolio tail risk

“…As previously reported in the literature, see Haas et al (2004) for an overview, the mixture of normal distributions provides a reasonably good approximation to the returns distribution.…”

“…We estimate the tail of the distribution of the portfolio losses using the semiparametric estimator, and compare it with a Student-t and a mixture of four normal distributions. A review of the relevant properties and results on using a mixture of normal distributions to model the unconditional distribution of asset returns can be found in Haas et al (2004) and references therein. We compute the VaR for the ten, fifty and one hundred component portfolios, at the levels of 99%, 97.5%, 95%…”

Asymmetric multivariate normal mixture GARCH

“…Nevertheless, the overall process can still be stationary, as long as the corresponding mixing weights are sufficiently small. This has also been noted by and parallels the situation in the univariate case (see Haas et al, 2004;and Alexander and Lazar, 2006).…”

“…A general univariate normal mixture GARCH model, generalizing earlier specifications such as Vlaar and Palm (1993) and Wong and Li (2001), has been proposed by Haas et al (2004) and Alexander and Lazar (2006) and further investigated by Alexander and Lazar (2005), Ausin and Galeano (2007), Bertholon et al (2006), Haas et al (2006a), , Wu and Lee (2007), and Giannikis et al (2008).…”

“…For example, in applications to portfolio management, correlations between assets are often of predominant interest. Quite recently, in order to cope with such situations, proposed a multivariate version of the normal mixture GARCH model developed in Haas et al (2004) and Alexander and Lazar (2006), investigated its fourthmoment structure and demonstrated its practicability in an application to a bivariate stock return series.…”