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Modeling the Volatility and Expected Value of a Diversified World Index

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This paper considers a diversified world stock index in a continuous financial market with the growth optimal portfolio (GOP) as the reference unit or benchmark. Diversified broadly based portfolios, which include major world stock market indices, are shown to approximate the GOP. It is demonstrated that a key financial quantity is the drift of the discounted GOP, which can be expressed explicitly using a certain quadratic variation term. Using real market approximations for the discounted GOP it is shown that its drift does not vary greatly in the long term. For a diversified world index this leads to a natural model where the discounted index is a time transformed squared Bessel process of dimension four. The inverse of the squared GOP volatility then follows a square root process of dimension four.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp103.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 103.

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Date of creation: 01 Jun 2003
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Handle: RePEc:uts:rpaper:103

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Keywords: world index; volatility; benchmark model; growth optimal portfolio; bessel process; square root process;

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  1. Eckhard Platen, 2003. "Diversified Portfolios in a Benchmark Framework," Research Paper Series 87, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
  3. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  4. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
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