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2015 | OriginalPaper | Buchkapitel

52. Modeling Multiple Asset Returns by a Time-Varying t Copula Model

verfasst von : Long Kang

Erschienen in: Handbook of Financial Econometrics and Statistics

Verlag: Springer New York

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Abstract

We illustrate a framework to model joint distributions of multiple asset returns using a time-varying Student’s t copula model. We model marginal distributions of individual asset returns by a variant of GARCH models and then use a Student’s t copula to connect all the margins. To build a time-varying structure for the correlation matrix of t copula, we employ a dynamic conditional correlation (DCC) specification. We illustrate the two-stage estimation procedures for the model and apply the model to 45 major US stocks returns selected from nine sectors. As it is quite challenging to find a copula function with very flexible parameter structure to account for difference dependence features among all pairs of random variables, our time-varying t copula model tends to be a good working tool to model multiple asset returns for risk management and asset allocation purposes. Our model can capture time-varying conditional correlation and some degree of tail dependence, while it also has limitations of featuring symmetric dependence and inability of generating high tail dependence when being used to model a large number of asset returns.

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Alternative approaches are also developed, such as in Ang and Bekaert (2002), Goeij and Marquering (2004), and Lee and Long (2009), to address non-normal joint distributions of asset returns.

For a detailed survey on the estimation of Copula-GARCH model, see Chap. 5 of Cherubini et al. (2004).

See Hamilton (1994) and Greene (2003) for more details on maximum likelihood estimation.

See Nelsen (1998) and Joe (1997) for a formal treatment of copula theory, and Bouye et al. (2000), Cherubini et al. (2004), and Embrechts et al. (2002) for applications of copula theory in finance.

See Patton (2004).

See Glosten et al. (1993).

In contrast to the previous standardized Student’s t distribution, the standard Student’s t distribution here has variance as v/(v−2).

Please see Engle and Sheppard (2001) and Engle (2002) for details on the multivariate DCC-GARCH models.

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Titel: Modeling Multiple Asset Returns by a Time-Varying t Copula Model
verfasst von: Long Kang
Verlag: Springer New York
Buch: Handbook of Financial Econometrics and Statistics
Print ISBN: 978-1-4614-7749-5

Electronic ISBN: 978-1-4614-7750-1

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-1-4614-7750-1_52