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Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices

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Abstract

The aim of this paper is to document some empirical facts related to log-returns of diversified world stock indices when these are denominated in different currencies. Motivated by earlier results, we have obtained the estimated distribution of log-returns for a range of world stock indices over long observation periods. We expand previous studies by applying the maximum likelihood ratio test to the large class of generalized hyperbolic distributions, and investigate the log-returns of a variety of diversified world stock indices in different currency denominations. This identifies the Student-t distribution with about four degrees of freedom as the typical estimated log-return distribution of such indices. Owing to the observed high levels of significance, this result can be interpreted as a stylized empirical fact.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp194.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 194.

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Length: 24
Date of creation: 01 Mar 2007
Date of revision:
Handle: RePEc:uts:rpaper:194

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Keywords: diversified world stock index; growth optimal portfolio; log-return distribution; Student-t distribution; generalized hyperbolic distribution; likelihood ratio test;

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References

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  1. 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 637-54, May-June.
  2. Eckhard Platen & Gerhard Stahl, 2003. "A Structure for General and Specific Market Risk," Research Paper Series 91, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Leah Kelly & Eckhard Platen, 2003. "Estimating for Discretely Observed Diffusions Using Transform Functions," Research Paper Series 96, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Damir Filipović & Eckhard Platen, 2009. "Consistent Market Extensions Under The Benchmark Approach," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 41-52.
  5. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  6. 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 244-80, April.
  7. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 180, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  9. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 1-22, March.
  10. Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
  11. Eckhard Platen, 2003. "Modeling the Volatility and Expected Value of a Diversified World Index," Research Paper Series 103, Quantitative Finance Research Centre, University of Technology, Sydney.
  12. Kevin Fergusson & Eckhard Platen, 2005. "On the Distributional Characterization of Log-returns of a World Stock Index," Research Paper Series 153, Quantitative Finance Research Centre, University of Technology, Sydney.
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Cited by:
  1. Ignatieva, Katja & Platen, Eckhard, 2012. "Estimating the diffusion coefficient function for a diversified world stock index," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1333-1349.
  2. Suárez-García, Pablo & Gómez-Ullate, David, 2013. "Scaling, stability and distribution of the high-frequency returns of the Ibex35 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1409-1417.
  3. Pablo Su\'arez-Garc\'ia & David G\'omez-Ullate, 2012. "Scaling, stability and distribution of the high-frequency returns of the IBEX35 index," Papers 1208.0317, arXiv.org.
  4. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Katja Ignatieva & Eckhard Platen, 2009. "Modelling Co-movements and Tail Dependency in the International Stock Market via Copulae," Research Paper Series 265, Quantitative Finance Research Centre, University of Technology, Sydney.
  6. Carl Chiarella & Jonathan Ziveyi, 2011. "Two Stochastic Volatility Processes - American Option Pricing," Research Paper Series 292, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Jan Baldeaux & Eckhard Platen, 2013. "Liability Driven Investments under a Benchmark Based Approach," Research Paper Series 325, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. Ke Du & Eckhard Platen & Renata Rendek, 2012. "Modeling of Oil Prices," Research Paper Series 321, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Daniel T. Cassidy & Michael J. Hamp & Rachid Ouyed, 2010. "Student's t-Distribution Based Option Sensitivities: Greeks for the Gosset Formulae," Papers 1003.1344, arXiv.org, revised Jul 2010.

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