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On the Distributional Characterization of Daily Log-Returns of a World Stock Index

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Author Info

  • Kevin Fergusson
  • Eckhard Platen

Abstract

In this paper distributions are identified which suitably fit log-returns of the world stock index when these are expressed in units of different currencies. By searching for a best fit in the class of symmetric generalized hyperbolic distributions the maximum likelihood estimates appear to cluster in the neighbourhood of those of the Student t distribution. This is confirmed at a high significance level under the likelihood ratio test. Finally, the paper derives the minimal market model, which explains the empirical findings as a consequence of the optimal market dynamics.

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File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500394052
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 13 (2006)
Issue (Month): 1 ()
Pages: 19-38

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Handle: RePEc:taf:apmtfi:v:13:y:2006:i:1:p:19-38

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Web page: http://www.tandfonline.com/RAMF20

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Related research

Keywords: World stock index; log-return distribution; Student t distribution; symmetric generalized hyperbolic distribution;

References

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  1. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 2: Empirical Results," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 221-47, November.
  2. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
  3. 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.
  4. Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
  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. 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.
  7. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Research Paper Series 129, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 1: Principles of Inference," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 207-19, November.
  9. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
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Citations

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Cited by:
  1. Thomas Lux, 2008. "Stochastic Behavioral Asset Pricing Models and the Stylized Facts," Kiel Working Papers 1426, Kiel Institute for the World Economy.
  2. Schuhmacher, Frank & Eling, Martin, 2011. "Sufficient conditions for expected utility to imply drawdown-based performance rankings," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2311-2318, September.
  3. Aki-Hiro Sato & Takaki Hayashi & Janusz A. Ho{\l}yst, 2012. "Comprehensive Analysis of Market Conditions in the Foreign Exchange Market: Fluctuation Scaling and Variance-Covariance Matrix," Papers 1204.0426, arXiv.org.
  4. William T. Shaw, 2011. "Risk, VaR, CVaR and their associated Portfolio Optimizations when Asset Returns have a Multivariate Student T Distribution," Papers 1102.5665, arXiv.org.
  5. repec:hal:journl:halshs-00281585 is not listed on IDEAS
  6. Aki-Hiro Sato & Takaki Hayashi & Janusz HoƂyst, 2012. "Comprehensive analysis of market conditions in the foreign exchange market," Journal of Economic Interaction and Coordination, Springer, vol. 7(2), pages 167-179, October.
  7. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. Turnbull, Bradley C. & Ghosh, Sujit K., 2014. "Unimodal density estimation using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 13-29.

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