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Intraday Empirical Analysis and Modeling of Diversified World Stock Indices

  • Wolfgang Breymann
  • Leah Kelly
  • Eckhard Platen

This paper proposes an approach to the intraday analysis of diversified world stock accumulation indices. The growth optimal portfolio (GOP) is used as reference unit or benchmark in a continuous financial market model. Diversified portfolios, covering the world stock market, are constructed and shown to approximate the GOP, providing the basis for a range of financial applications. The normalized GOP is modeled as a time transformed square root process of dimension four. Its dynamics are empirically verified for several world stock indices. Furthermore, the evolution of the transformed time is modeled as the integral over a rapidly evolving mean-reverting market activity process with deterministic volatility. The empirical findings suggest a rather simple and robust model for a world stock index that reflects the historical evolution, by using only a few readily observable parameters.

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File URL: http://hdl.handle.net/10.1007/s10690-006-9010-0
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Article provided by Springer in its journal Asia-Pacific Financial Markets.

Volume (Year): 12 (2005)
Issue (Month): 1 (March)
Pages: 1-28

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Handle: RePEc:kap:apfinm:v:12:y:2005:i:1:p:1-28
Contact details of provider: Web page: http://springerlink.metapress.com/link.asp?id=102851

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  1. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  2. 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.
  3. W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 1-14.
  4. 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.
  5. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204.
  6. Olivier V. Pictet & Michel M. Dacorogna & Ulrich A. Muller, 1996. "Hill, Bootstrap and Jackknife Estimators for Heavy Tails," Working Papers 1996-12-10, Olsen and Associates.
  7. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. Goodhart, Charles A. E. & O'Hara, Maureen, 1997. "High frequency data in financial markets: Issues and applications," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 73-114, June.
  9. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  10. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney.
  11. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
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