A skewed GARCH-type model for multivariate financial time series

Franceschini, Cinzia; Loperfido, Nicola

doi:10.1007/978-88-470-1481-7_15

Cited by 5 publications

(7 citation statements)

References 13 publications

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“…In the first place, it shows that the third cumulant of the multivariate SGARCH model proposed by De Luca, Genton, and Loperfido (2006) is identified by a limited number of parameters, thus avoiding the curse of dimensionality when modelling multivariate skewness. In the second place, it gives a theoretical justification to the empirical results in Franceschini and Loperfido (2010) and generalizes a result in De Luca and Loperfido (2004), by showing that the third cumulant of a multivariate SGARCH model is a matrix with either null or negative elements.…”

Section: Introductionsupporting

confidence: 56%

“…The third cumulant of a multivariate SN random vector z ∼ SN n (ξ , , α) has a very simple form (Franceschini and Loperfido 2010):…”

Section: Multivariate Skewness For the Sgarch Modelmentioning

confidence: 99%

“…In the univariate case, however, its formulation is quite cumbersome. Hidden truncation models are closed under linear transformations and their third cumulant have a simple analytical form (Genton, He, and Liu 2001; Mallick 2003, 2009;Franceschini and Loperfido 2010). In particular, the multivariate skew-normal (Azzalini and Dalla Valle 1996), the generalized skew-normal (Arnold and Beaver 2000) and the multivariate skew-t (Branco and Dey 2001) are three of the few coherent and tractable multivariate models for asset returns.…”

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confidence: 99%

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Modelling multivariate skewness in financial returns: a SGARCH approach

Luca

Loperfido

2012

The European Journal of Finance

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Skewness of financial time series is a relevant topic, due to its implications for portfolio theory and for statistical inference. In the univariate case, its default measure is the third cumulant of the standardized random variable. It can be generalized to the third multivariate cumulant that is a matrix containing all\ud centered moments of order three which can be obtained from a random vector. The present paper examines some properties of the third cumulant under the assumptions of the multivariate SGARCH model introduced by De Luca, Genton, and Loperfido [2006.Amultivariate skew-GARCH model. Advances in Econometrics 20: 33–57]. In the first place, it allows for parsimonious modelling of multivariate skewness. In the second place, all its elements are either null or negative, consistently with previous empirical and theoretical findings. A numerical example with financial returns of France, Spain and Netherlands illustrates the theoretical results in the paper

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Section: Introductionsupporting

confidence: 56%

“…The third cumulant of a multivariate SN random vector z ∼ SN n (ξ , , α) has a very simple form (Franceschini and Loperfido 2010):…”

Section: Multivariate Skewness For the Sgarch Modelmentioning

confidence: 99%

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confidence: 99%

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Modelling multivariate skewness in financial returns: a SGARCH approach

Luca

Loperfido

2012

The European Journal of Finance

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“…Using other distributions and, in particular, non-parametric tests, he concludes that daily returns are symmetric in most markets. Franceschini and Loperfido (2010) report tests for multivariate skewness based on the skew-normal distribution.…”

Section: Empirical Studies Of Skewnessmentioning

confidence: 99%

“…De Luca, Genton, and Loperfido (2006) describe a multivariate skew-GARCH model. A multivariate skew-GARCH model for financial times series is described in Franceschini and Loperfido (2010). Other papers concerned with skewness in the context of times series include well-known works by Bauwens and Laurent (2005) and Jondeau and Rockinger (2003, 2006b, 2012.…”

Section: Time Series Models and Other Applicationsmentioning

confidence: 99%

Skewed distributions in finance and actuarial science: a review

Adcock

Eling

Loperfido

2012

The European Journal of Finance

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125

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That the returns on financial assets and insurance claims are not well described by the multivariate normal distribution is generally acknowledged in the literature. This paper presents a review of the use of the skew-normal distribution and its extensions in finance and actuarial science, highlighting known results as well as potential directions for future research. When skewness and kurtosis are present in asset returns, the skew-normal and skew-Student distributions are natural candidates in both theoretical and empirical work. Their parameterization is parsimonious and they are mathematically tractable. In finance, the distributions are interpretable in terms of the efficient markets hypothesis. Furthermore, they lead to theoretical results that are useful for portfolio selection and asset pricing. In actuarial science, the presence of skewness and kurtosis in insurance claims data is the main motivation for using the skew-normal distribution and its extensions. The skew-normal has been used in studies on risk measurement and capital allocation, which are two important research fields in actuarial science. Empirical studies consider the skew-normal distribution because of its flexibility, interpretability, and tractability. This paper comprises four main sections: an overview of skew-normal distributions; a review of skewness in finance, including asset pricing, portfolio selection, time series modeling, and a review of its applications in insurance, in which the use of alternative distribution functions is widespread. The final section summarizes some of the challenges associated with the use of skew-elliptical distributions and points out some directions for future research. C. Adcock et al.those of Arditti and Levy (1975) and Kraus and Litzenberger (1976), marks the point at which the modern theory of finance started revealing evidence of skewness analogous to that provided by Markowitz, Sharpe, Lintner, Tobin, and others.In the context of actuarial science, it is important to recognize that insurance risks have skewed distributions (see, for example, Lane 2000), which is why in many cases, the classical normal distribution is an inadequate model for insurance risks or losses. Some insurance risks also exhibit heavy tails, especially those exposed to catastrophes (see Embrechts, McNeil, and Straumann 2002). The skew-normal distribution and its extensions thus might be promising since they preserve the advantages of the normal distribution with the additional benefit of flexibility with regard to skewness and kurtosis. The skew-normal distribution and its extensions have been used recently in studies on risk management, capital allocation, and goodness-of-fit (Vernic 2006;Bolance et al. 2008;Eling 2012).This review paper is motivated by the belief that asymmetry in asset returns, and skewness in particular, is an important field of research. Such research has two clear themes. The first is the never-ending and entirely natural wish to develop better univariate models for asset returns. Such model developme...

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Portfolio optimisation under flexible dynamic dependence modelling

Bernardi

Catania

2018

Journal of Empirical Finance

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Signals coming from multivariate higher order conditional moments as well as the information contained in exogenous covariates, can be effectively exploited by rational investors to allocate their wealth among different risky investment opportunities. This paper proposes a new flexible dynamic copula model being able to explain and forecast the time-varying shape of large dimensional asset returns distributions. Moreover, we let the univariate marginal distributions to be driven by an updating mechanism based on the scaled score of the conditional distribution. This framework allows us to introduce time-variation in up to the fourth moment of the conditional distribution. The time-varying dependence pattern is subsequently modelled as function of a latent Markov Switching process, allowing also for the inclusion of exogenous covariates in the dynamic updating equation. We empirically assess that the proposed model substantially improves the optimal portfolio allocation of rational investors maximising their expected utility.

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A skewed GARCH-type model for multivariate financial time series

Cited by 5 publications

References 13 publications

Modelling multivariate skewness in financial returns: a SGARCH approach

Modelling multivariate skewness in financial returns: a SGARCH approach

Skewed distributions in finance and actuarial science: a review

Portfolio optimisation under flexible dynamic dependence modelling

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