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Open AccessOpen Access JUSTC Research Articles:Management Science and Engineering

Analysis of portfolio VaR by pair copula-LMSV-t

  • Dept. of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.12.010
  • Received Date: 11 October 2014
  • Accepted Date: 23 June 2015
  • Rev Recd Date: 23 June 2015
  • Publish Date: 30 December 2015
    Abstract

  • Abstract

    The LMSV-t model was adopted to estimate the marginal distribution, instead of the GARCH model, which has been adopted before, and the pair copula-LMSV-t model was constructed. Furthermore, the method for parameter estimation of LMSV-t by MCMC was offered. An empirical example with the open-end fund's data demonstrates the superiority of the LMSV-t model in describing the volatility and long memory of asset's return. Using the LMSV-t model as the description of the marginal distribution, the pair copula-LMSV-t model has better performance in the analysis of portfolio VaR.

    Abstract

    The LMSV-t model was adopted to estimate the marginal distribution, instead of the GARCH model, which has been adopted before, and the pair copula-LMSV-t model was constructed. Furthermore, the method for parameter estimation of LMSV-t by MCMC was offered. An empirical example with the open-end fund's data demonstrates the superiority of the LMSV-t model in describing the volatility and long memory of asset's return. Using the LMSV-t model as the description of the marginal distribution, the pair copula-LMSV-t model has better performance in the analysis of portfolio VaR.
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    • References(16)
  • [1]
    Aas K, Czado C, Frigessi A, et al. Pair-copula constructions of multiple dependence [J]. Insurance: Mathematics and Economics, 2009, 44(2): 182-198.
    [2]
    de Melo Mendes B V, Semeraro M M, Leal R P C. Pair-copulas modeling in finance [J]. Financial Markets and Portfolio Management, 2010, 2(24):193-213.
    [3]
    Hofmann M, Czado C. Assessing the VaR of a portfolio using D-vine copula based multivariate GARCH models[R/OL]. doi: 10.1.1.176.6447.
    [4]
    Huang Enxi, Cheng Xijun. Analysis of portfolio VaR by pair copula-GARCH[J]. Journal of the Graduate School of the Chinese Academy of Sciences, 2010, 27(4): 440-447.
    黄恩喜, 程希骏. 基于pair copula-GARCH模型的多资产组合VaR分析[J]. 中国科学院研究生院学报, 2010, 27(4): 440-447.
    [5]
    Chen Qinping, Chen Xijun. A study on pair-copula constructions of multiple dependence[J]. Jouranl of Applied Statistics and Management, 2013, 32(2):232-239.
    陈清平, 程希骏. 一个基于pair-copula法构建高维相依结构的研究[J]. 数理统计与管理, 2013,32(2):232-239.
    [6]
    Durbin J, Koopman S J. Monte Carlo maximum likelihood estimation for non-Gaussian state space models [J]. Biometrika, 1997, 84(3): 669-684.
    [7]
    Kim S, Shephard N, Chib S. Stochastic volatility: likelihood inference and comparison with ARCH models [J]. The Review of Economic Studies, 1998(65):361-393.
    [8]
    Yu Suhong, Zhang Shiying. The Comparative research between the SV and GARCH models on their abilities to describe financial time series[J]. Systems Engineering, 2002,20(5): 28-33.
    余素红, 张世英. SV与GARCH模型对金融时间序列刻画能力的比较研究[J].系统工程, 2002,20(5): 28-33.
    [9]
    Breidt F J, Crato N, de Lima P. The detection and estimation of long memory in stochastic volatility[J]. Econometrics, 1998(83): 325-348.
    [10]
    Ghysels E, Harvey, Renault E. Stochastic volatility[M]// Handbook of Statistics, Vol. 14. Berlin: Elsevier Science BV, 1996:119-191.
    [11]
    Jacquier E, Polson N G, Rossi P E. Bayesian analysis of stochastic volatility models[J]. Journal of Business & Economic Statistics, 2002, 20(1): 69-87.
    [12]
    Spiegelhalter D J, Best N G, Carlin B P, et al. Bayesian measures of model complexity and fit [J]. Journal of the Royal Statistical Society, Series B, 2002(64):583-639.
    [13]
    Wang Yue, Cheng Xijun, Ma Lijun. Dependence analysis of SZI & HSI based on the two-parameter Copula[J]. Mathematics in Practice and Theory, 2011, 41(17): 1-7.
    王玥,程希骏,马利军. 基于双参数Copula沪港股市的相关性分析[J]. 数学的实践与认识, 2011,41(17): 1-7.
    [14]
    Czado C, Schepsmeier U, Min A. Maximum likelihood estimation of mixed C-vines with application to exchange rates [J]. Statistical Modelling, 2012, 12(3): 229-255.
    [15]
    Kupiec P H. Techniques for verifying the accuracy of risk measurement models[J]. The Journal of Derivatives, 1995, 3(2):73-84.
    [16]
    Christoffersen P F. Evaluating interval forecasts[J]. International Economic Review, 1998: 39(4)：841-862.
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    [1]
    Aas K, Czado C, Frigessi A, et al. Pair-copula constructions of multiple dependence [J]. Insurance: Mathematics and Economics, 2009, 44(2): 182-198.
    [2]
    de Melo Mendes B V, Semeraro M M, Leal R P C. Pair-copulas modeling in finance [J]. Financial Markets and Portfolio Management, 2010, 2(24):193-213.
    [3]
    Hofmann M, Czado C. Assessing the VaR of a portfolio using D-vine copula based multivariate GARCH models[R/OL]. doi: 10.1.1.176.6447.
    [4]
    Huang Enxi, Cheng Xijun. Analysis of portfolio VaR by pair copula-GARCH[J]. Journal of the Graduate School of the Chinese Academy of Sciences, 2010, 27(4): 440-447.
    黄恩喜, 程希骏. 基于pair copula-GARCH模型的多资产组合VaR分析[J]. 中国科学院研究生院学报, 2010, 27(4): 440-447.
    [5]
    Chen Qinping, Chen Xijun. A study on pair-copula constructions of multiple dependence[J]. Jouranl of Applied Statistics and Management, 2013, 32(2):232-239.
    陈清平, 程希骏. 一个基于pair-copula法构建高维相依结构的研究[J]. 数理统计与管理, 2013,32(2):232-239.
    [6]
    Durbin J, Koopman S J. Monte Carlo maximum likelihood estimation for non-Gaussian state space models [J]. Biometrika, 1997, 84(3): 669-684.
    [7]
    Kim S, Shephard N, Chib S. Stochastic volatility: likelihood inference and comparison with ARCH models [J]. The Review of Economic Studies, 1998(65):361-393.
    [8]
    Yu Suhong, Zhang Shiying. The Comparative research between the SV and GARCH models on their abilities to describe financial time series[J]. Systems Engineering, 2002,20(5): 28-33.
    余素红, 张世英. SV与GARCH模型对金融时间序列刻画能力的比较研究[J].系统工程, 2002,20(5): 28-33.
    [9]
    Breidt F J, Crato N, de Lima P. The detection and estimation of long memory in stochastic volatility[J]. Econometrics, 1998(83): 325-348.
    [10]
    Ghysels E, Harvey, Renault E. Stochastic volatility[M]// Handbook of Statistics, Vol. 14. Berlin: Elsevier Science BV, 1996:119-191.
    [11]
    Jacquier E, Polson N G, Rossi P E. Bayesian analysis of stochastic volatility models[J]. Journal of Business & Economic Statistics, 2002, 20(1): 69-87.
    [12]
    Spiegelhalter D J, Best N G, Carlin B P, et al. Bayesian measures of model complexity and fit [J]. Journal of the Royal Statistical Society, Series B, 2002(64):583-639.
    [13]
    Wang Yue, Cheng Xijun, Ma Lijun. Dependence analysis of SZI & HSI based on the two-parameter Copula[J]. Mathematics in Practice and Theory, 2011, 41(17): 1-7.
    王玥,程希骏,马利军. 基于双参数Copula沪港股市的相关性分析[J]. 数学的实践与认识, 2011,41(17): 1-7.
    [14]
    Czado C, Schepsmeier U, Min A. Maximum likelihood estimation of mixed C-vines with application to exchange rates [J]. Statistical Modelling, 2012, 12(3): 229-255.
    [15]
    Kupiec P H. Techniques for verifying the accuracy of risk measurement models[J]. The Journal of Derivatives, 1995, 3(2):73-84.
    [16]
    Christoffersen P F. Evaluating interval forecasts[J]. International Economic Review, 1998: 39(4)：841-862.
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