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Approximation of Asymmetric Multivariate Return Distributions

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  • Ba Chu

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    Abstract

    We develop a new method to approximate the asymmetric multivariate probability density function (pdf) of financial asset returns by using series expansions; a rate of convergence for the mean absolute error of this approximation is also provided. We then propose the method of maximum likelihood and the generalized method of moments to estimate the parameters of the approximated pdf. A Monte-Carlo experiment corroborates the feasibility of our approach. Copyright Springer Science+Business Media, LLC. 2012

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    File URL: http://hdl.handle.net/10.1007/s10690-011-9150-8
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    Bibliographic Info

    Article provided by Springer in its journal Asia-Pacific Financial Markets.

    Volume (Year): 19 (2012)
    Issue (Month): 3 (September)
    Pages: 293-318

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    Handle: RePEc:kap:apfinm:v:19:y:2012:i:3:p:293-318

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    Web page: http://springerlink.metapress.com/link.asp?id=102851

    Related research

    Keywords: Edge worth expansion; Series approximation; Asymmetric dependence; Tail risk; Mixture of the Gamma distributions; Laguerre polynomials; C60; C13; G11;

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    1. Knight, J.L. & Stachell, S.E. & Tran, K.C., 1995. "Statistical Modeling of Asymetric Risk in Asset Returns," Papers 95-3, Saskatchewan - Department of Economics.
    2. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    3. Andrew J. Patton, 2002. "On the out-of-sample importance of skewness and asymetric dependence for asset allocation," LSE Research Online Documents on Economics 24951, London School of Economics and Political Science, LSE Library.
    4. Okimoto, Tatsuyoshi, 2008. "New Evidence of Asymmetric Dependence Structures in International Equity Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 43(03), pages 787-815, September.
    5. Chu, Ba, 2011. "Recovering copulas from limited information and an application to asset allocation," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1824-1842, July.
    6. Y. Malevergne & D. Sornette, 2002. "Multi-Moments Method for Portfolio Management: Generalized Capital Asset Pricing Model in Homogeneous and Heterogeneous markets," Papers cond-mat/0207475, arXiv.org.
    7. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-48, May.
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