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Subordinated Market Index Models: A Comparison

Author

Listed:
  • SIMON HURST

    ()

  • ECKHARD PLATEN

    ()

  • SVETLOZAR RACHEV

    ()

Abstract

The paper compares various processes subordinated to the Wiener process to model the leptokurtic characteristics of index returns. Empirical analysis is performed on the Dow Jones and Nikkei 225 indexes. A good model to capture the typical tail behaviour of these indexes turns out to be a long Student t distributed one. Copyright Kluwer Academic Publishers 1997

Suggested Citation

  • Simon Hurst & Eckhard Platen & Svetlozar Rachev, 1997. "Subordinated Market Index Models: A Comparison," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 4(2), pages 97-124, May.
  • Handle: RePEc:kap:apfinm:v:4:y:1997:i:2:p:97-124
    DOI: 10.1023/A:1009650313980
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    References listed on IDEAS

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    1. Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393-393.
    2. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    3. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    6. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    Citations

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    Cited by:

    1. Fung, Thomas & Seneta, Eugene, 2010. "Extending the multivariate generalised t and generalised VG distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 154-164, January.
    2. Stoyan Stoyanov & Borjana Racheva-Iotova & Svetlozar Rachev & Frank Fabozzi, 2010. "Stochastic models for risk estimation in volatile markets: a survey," Annals of Operations Research, Springer, vol. 176(1), pages 293-309, April.
    3. Burq, Zaeem A. & Jones, Owen D., 2008. "Simulation of Brownian motion at first-passage times," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 64-71.
    4. Fabozzi Frank J. & Stoyanov Stoyan V. & Rachev Svetlozar T., 2013. "Computational aspects of portfolio risk estimation in volatile markets: a survey," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(1), pages 103-120, February.
    5. Thomas Fung & Eugene Seneta, 2010. "Tail dependence and skew distributions," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 327-333.
    6. Gao, Jiti, 2002. "Modeling long-range dependent Gaussian processes with application in continuous-time financial models," MPRA Paper 11973, University Library of Munich, Germany, revised 18 Sep 2003.
    7. David Heath & Simon Hurst & Eckhard Platen, 1999. "Modelling the Stochastic Dynamics of Volatility for Equity Indices," Research Paper Series 7, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Yoshio Miyahara & Alexander Novikov, 2001. "Geometric Lévy Process Pricing Model," Research Paper Series 66, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Michele Leonardo Bianchi & Frank J. Fabozzi & Svetlozar T. Rachev, 2014. "Calibrating the Italian smile with time-varying volatility and heavy-tailed models," Temi di discussione (Economic working papers) 944, Bank of Italy, Economic Research and International Relations Area.
    10. Richard Finlay & Eugene Seneta, 2008. "Stationary-Increment Variance-Gamma and "t" Models: Simulation and Parameter Estimation," International Statistical Review, International Statistical Institute, vol. 76(2), pages 167-186, August.
    11. Sebastian Orzel & Aleksander Weron, 2009. "Calibration of the subdiffusive Black–Scholes model," HSC Research Reports HSC/09/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    12. Evis Këllezi & Nick Webber, 2004. "Valuing Bermudan options when asset returns are Levy processes," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 87-100.
    13. Mercik, Szymon & Weron, Rafal, 2002. "Origins of scaling in FX markets," MPRA Paper 2294, University Library of Munich, Germany.
    14. Grothe, Oliver & Schmidt, Rafael, 2010. "Scaling of Lévy–Student processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1455-1463.
    15. De Giovanni, Domenico & Ortobelli, Sergio & Rachev, Svetlozar, 2008. "Delta hedging strategies comparison," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1615-1631, March.
    16. Steven Kou, 2000. "A Jump Diffusion Model for Option Pricing with Three Properties: Leptokurtic Feature, Volatility Smile, and Analytical Tractability," Econometric Society World Congress 2000 Contributed Papers 0062, Econometric Society.

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