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CN 34-1054/N

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Risk measurement and backtesting of financial market based on E-GAS-AST model

  • School of Management, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.05.013
  • Received Date: 01 May 2019
  • Accepted Date: 03 June 2019
  • Rev Recd Date: 03 June 2019
  • Publish Date: 31 May 2020
    Abstract

  • Abstract

    Concerning financial data's fat-tail,volatility clustering and asymmetry, we raise two data-driven models: E-GAS-AST model and E-GAS-AST-GPD model,and proceed risk measuring and backtesting with real data. Based on generalized autoregressive score(GAS) model,combining asymmetric student-t (AST) distribution with heavy tail,we propose an new model denoted by E-GAS-AST referring to EGARCH model.Considering describing more of tail features,we propose another E-GAS-AST-GPD model with generalized pareto distribution (GPD).Afterwards,the paper computes VaR and ES by studying distributions of residuals,and backtests them separately.Introducing parameter-driven models,such as semi-parameter generalized autoregressive conditional heteroskedasticity(GARCH) model,EGARCH-t model and GJR-GARCH-t model to produce risk measurement we compare them with two above models proposed.Empirical analysis using Dow Jones Index and Shanghai Stock Exchange Composite Index concerning change point reveals E-GAS-AST model is proper to model financial market and measure risk.

    Abstract

    Concerning financial data's fat-tail,volatility clustering and asymmetry, we raise two data-driven models: E-GAS-AST model and E-GAS-AST-GPD model,and proceed risk measuring and backtesting with real data. Based on generalized autoregressive score(GAS) model,combining asymmetric student-t (AST) distribution with heavy tail,we propose an new model denoted by E-GAS-AST referring to EGARCH model.Considering describing more of tail features,we propose another E-GAS-AST-GPD model with generalized pareto distribution (GPD).Afterwards,the paper computes VaR and ES by studying distributions of residuals,and backtests them separately.Introducing parameter-driven models,such as semi-parameter generalized autoregressive conditional heteroskedasticity(GARCH) model,EGARCH-t model and GJR-GARCH-t model to produce risk measurement we compare them with two above models proposed.Empirical analysis using Dow Jones Index and Shanghai Stock Exchange Composite Index concerning change point reveals E-GAS-AST model is proper to model financial market and measure risk.
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    • References(32)
  • [1]
    BROOKS C. Introductory Econometrics for Finance [M]. Cambridge University Press, 2019.
    [2]
    BLACK F. Studies in stock price volatility changes[C]//Proceedings of the 1976 Meeting of the Business & Economic Statistics. Washington: American Statistical Association, 1976: 177-81.
    [3]
    ENGLE R F. Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation[J]. Econometrica1981, 50: 987-1007.
    [4]
    BOLLERSLEV T. Generalized autoregressive conditional heteroscedasticity [J]. Journal of Econometrics, 1986, 31(3):307-327.
    [5]
    CREAL D, KOOPMAN S J, LUCAS A. Generalized autoregressive score models with applications [J]. Journal of Applied Econometrics, 2013, 28(5):777-795.
    [6]
    ENGLE R F, RUSSELL J R. Autoregressive conditional duration: A new model for irregularly spaced transaction data [J]. Econometrica, 1998, 66(5): 1127-1162.
    [7]
    PATTON A J. Modelling asymmetric exchange rate dependence. International economic review [J]. 2006, 47(2):527-556.
    [8]
    HANSEN B E. Autoregressive conditional density estimation [J]. International Economic Review, 1994, 35(3):705-730.
    [9]
    STEEL F. On bayesian modeling of fat tails and skewness [J]. Journal of the American Statistical Association, 1998, 93(441):359-371.
    [10]
    THEODOSSIOU P. Financial data and the skewed generalized t distribution [J]. Management Science, 1998, 44:1650-1661.
    [11]
    BRANCO M D, DEY D K. A general class of multivariate skew-elliptical distributions [J]. Journal of Multivariate Analysis, 2001, 79(1):99-113.
    [12]
    BAUWENS L, LAURENT S. A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity models[J]. Journal of Business and Economic Statistics, 2005, 23(3):346-354.
    [13]
    JONES M C, FADDY M J. A skew extension of the t-distribution, with applications [J]. Journal of the Royal Statistical Society，2003, 65(1):159-174.
    [14]
    SAHU S K, DEY D K, BRANCO M D. A new class of multivariate skew distributions with applications to bayesian regression models [J]. Canadian Journal of Statistics, 2003, 31(2):129-150.
    [15]
    AZZALINI A, CAPITANIO A. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution [J]. Journal of the Royal Statistical Society，2003, 65(2):367-389.
    [16]
    AAS K, HAFF I H. The generalized hyperbolic skew student's t-distribution [J].Journal of Financial Econometrics, 2006, 4(2):275-309.
    [17]
    ZHU D M, GALBRAITH J W. A generalized asymmetric student-t distribution with application to financial econometrics [J]. Journal of Econometrics, 2010, 157(2):297-305.
    [18]
    RIVAS D, CALEYO F, VALOR A, et al. Extreme value analysis applied to pitting corrosion experiments in low carbon steel: Comparison of block maxima and peak over threshold approaches [J]. Corrosion Science, 2008, 50(11):3193-3204.
    [19]
    LONGIN F. Value at risk: Une nouvelle approche fondée sur les valeurs extre＾mes [J]. Annales économie et de statistique, 1998，52: 23-51.
    [20]
    NEFTCI S N. Value at risk calculations, extreme events, and tail estimation [J]. Journal of Derivatives, 2000, 7(3):23-38.
    [21]
    FROMONT E. Modélisation des rentabiliteé extre＾mes des distributions de hedge funds [J]. Euro-Mediterranean Economics and Finance, 2005:126.
    [22]
    CARVALHAL A, MENDES B V M. Value-at-risk and extreme returns in Asian stock markets [J]. International Journal of Business, 2003, 8(1):17-40.
    [23]
    MCNEIL A J, FREY R. Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach [J]. Journal of Empirical Finance, 2000, 7(3-4):271-300.
    [24]
    MARIMOUTOU V, RAGGAD B, TRABELSI A. Extreme value theory and value at
    risk: Application to oil market [J]. Energy Economics, 2009, 31(4):519-530.
    [25]
    ASSAF A. Extreme observations and risk assessment in the equity markets of mena region: Tail measures and value-at-risk [J]. International Review of Financial Analysis, 2009, 18(3):109-116.
    [26]
    Pickands J Ⅲ. Statistical inference using extreme order statistics [J]. The Annals of Statistics, 1975, 3(1):119-131.
    [27]
    DUMOUCHEL W H. Estimating the stable index α in order to measure tail thickness: A critique [J]. The Annals of Statistics, 1983, 11(4):1019-1031.
    [28]
    PATTON A J, ZIEGEL J F, CHEN R. Dynamic semiparametric models for expected shortfall (and value-at-risk) [J]. Journal of Econometrics, 2019, 211(2): 388-413.
    [29]
    NELSON D B. Conditional heteroskedasticity in asset returns: A new approach [J]. Econometrica, 1991,59(2): 347-370.
    [30]
    GLOSTEN L R, JAGANNATHAN R, RUNKLE D E. On the relation between the expected value and the volatility of the nominal excess return on stocks [J]. The Journal of Finance, 1993, 48(5):1779-1801.
    [31]
    CATANIA L, BOUDT K, ARDIA D. GAS: Generalized Autoregressive Score Models[CP]. 2017.
    [32]
    EMBRECHTS P, KAUFMANN R, PATIE P. Strategic long-term financial risks: Single risk factors [J]. Computational Optimization and Applications, 2005, 32(1-2): 61-90.)
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    [1]
    BROOKS C. Introductory Econometrics for Finance [M]. Cambridge University Press, 2019.
    [2]
    BLACK F. Studies in stock price volatility changes[C]//Proceedings of the 1976 Meeting of the Business & Economic Statistics. Washington: American Statistical Association, 1976: 177-81.
    [3]
    ENGLE R F. Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation[J]. Econometrica1981, 50: 987-1007.
    [4]
    BOLLERSLEV T. Generalized autoregressive conditional heteroscedasticity [J]. Journal of Econometrics, 1986, 31(3):307-327.
    [5]
    CREAL D, KOOPMAN S J, LUCAS A. Generalized autoregressive score models with applications [J]. Journal of Applied Econometrics, 2013, 28(5):777-795.
    [6]
    ENGLE R F, RUSSELL J R. Autoregressive conditional duration: A new model for irregularly spaced transaction data [J]. Econometrica, 1998, 66(5): 1127-1162.
    [7]
    PATTON A J. Modelling asymmetric exchange rate dependence. International economic review [J]. 2006, 47(2):527-556.
    [8]
    HANSEN B E. Autoregressive conditional density estimation [J]. International Economic Review, 1994, 35(3):705-730.
    [9]
    STEEL F. On bayesian modeling of fat tails and skewness [J]. Journal of the American Statistical Association, 1998, 93(441):359-371.
    [10]
    THEODOSSIOU P. Financial data and the skewed generalized t distribution [J]. Management Science, 1998, 44:1650-1661.
    [11]
    BRANCO M D, DEY D K. A general class of multivariate skew-elliptical distributions [J]. Journal of Multivariate Analysis, 2001, 79(1):99-113.
    [12]
    BAUWENS L, LAURENT S. A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity models[J]. Journal of Business and Economic Statistics, 2005, 23(3):346-354.
    [13]
    JONES M C, FADDY M J. A skew extension of the t-distribution, with applications [J]. Journal of the Royal Statistical Society，2003, 65(1):159-174.
    [14]
    SAHU S K, DEY D K, BRANCO M D. A new class of multivariate skew distributions with applications to bayesian regression models [J]. Canadian Journal of Statistics, 2003, 31(2):129-150.
    [15]
    AZZALINI A, CAPITANIO A. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution [J]. Journal of the Royal Statistical Society，2003, 65(2):367-389.
    [16]
    AAS K, HAFF I H. The generalized hyperbolic skew student's t-distribution [J].Journal of Financial Econometrics, 2006, 4(2):275-309.
    [17]
    ZHU D M, GALBRAITH J W. A generalized asymmetric student-t distribution with application to financial econometrics [J]. Journal of Econometrics, 2010, 157(2):297-305.
    [18]
    RIVAS D, CALEYO F, VALOR A, et al. Extreme value analysis applied to pitting corrosion experiments in low carbon steel: Comparison of block maxima and peak over threshold approaches [J]. Corrosion Science, 2008, 50(11):3193-3204.
    [19]
    LONGIN F. Value at risk: Une nouvelle approche fondée sur les valeurs extre＾mes [J]. Annales économie et de statistique, 1998，52: 23-51.
    [20]
    NEFTCI S N. Value at risk calculations, extreme events, and tail estimation [J]. Journal of Derivatives, 2000, 7(3):23-38.
    [21]
    FROMONT E. Modélisation des rentabiliteé extre＾mes des distributions de hedge funds [J]. Euro-Mediterranean Economics and Finance, 2005:126.
    [22]
    CARVALHAL A, MENDES B V M. Value-at-risk and extreme returns in Asian stock markets [J]. International Journal of Business, 2003, 8(1):17-40.
    [23]
    MCNEIL A J, FREY R. Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach [J]. Journal of Empirical Finance, 2000, 7(3-4):271-300.
    [24]
    MARIMOUTOU V, RAGGAD B, TRABELSI A. Extreme value theory and value at
    risk: Application to oil market [J]. Energy Economics, 2009, 31(4):519-530.
    [25]
    ASSAF A. Extreme observations and risk assessment in the equity markets of mena region: Tail measures and value-at-risk [J]. International Review of Financial Analysis, 2009, 18(3):109-116.
    [26]
    Pickands J Ⅲ. Statistical inference using extreme order statistics [J]. The Annals of Statistics, 1975, 3(1):119-131.
    [27]
    DUMOUCHEL W H. Estimating the stable index α in order to measure tail thickness: A critique [J]. The Annals of Statistics, 1983, 11(4):1019-1031.
    [28]
    PATTON A J, ZIEGEL J F, CHEN R. Dynamic semiparametric models for expected shortfall (and value-at-risk) [J]. Journal of Econometrics, 2019, 211(2): 388-413.
    [29]
    NELSON D B. Conditional heteroskedasticity in asset returns: A new approach [J]. Econometrica, 1991,59(2): 347-370.
    [30]
    GLOSTEN L R, JAGANNATHAN R, RUNKLE D E. On the relation between the expected value and the volatility of the nominal excess return on stocks [J]. The Journal of Finance, 1993, 48(5):1779-1801.
    [31]
    CATANIA L, BOUDT K, ARDIA D. GAS: Generalized Autoregressive Score Models[CP]. 2017.
    [32]
    EMBRECHTS P, KAUFMANN R, PATIE P. Strategic long-term financial risks: Single risk factors [J]. Computational Optimization and Applications, 2005, 32(1-2): 61-90.)
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