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Modeling the Volatility and Expected Value of a Diversified World Index

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Author Info
Eckhard Platen () (School of Finance and Economics, University of Technology, Sydney)

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Abstract

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

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Find related papers by JEL classification:
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September. [Downloadable!] (restricted)
  2. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July. [Downloadable!] (restricted)
  3. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  4. Eckhard Platen, 2003. "Diversified Portfolios in a Benchmark Framework," Research Paper Series 87, Quantitative Finance Research Centre, University of Technology, Sydney.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Wolfgang Breymann & Leah Kelly & Eckhard Platen, 2004. "Intraday Empirical Analysis and Modeling of Diversified World Stock Indices," Research Paper Series 125, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
  2. David Heath & Eckhard Platen, 2004. "Understanding the Implied Volatility Surface for Options on a Diversified Index," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 55-77, March. [Downloadable!] (restricted)
    Other versions:
  3. Shane Miller & Eckhard Platen, 2004. "A Two-Factor Model for Low Interest Rate Regimes," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 107-133, March. [Downloadable!] (restricted)
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  4. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  5. David Heath & Eckhard Platen, 2004. "Local Volatility Function Models under a Benchmark Approach," Research Paper Series 124, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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  6. Eckhard Platen & Jason West, 2004. "A Fair Pricing Approach to Weather Derivatives," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 23-53, March. [Downloadable!] (restricted)
  7. David Heath & Eckhard Platen, 2005. "Currency Derivatives under a Minimal Market Model with Random Scaling," Research Paper Series 154, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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  8. Eckhard Platen, 2005. "On the Role of the Growth Optimal Portfolio in Finance," Research Paper Series 144, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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  9. Morten Christensen & Eckhard Platen, 2004. "A General Benchmark Model for Stochastic Jump Sizes," Research Paper Series 139, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  10. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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  11. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 184, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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  12. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2007. "Pricing under the Real-World Probability Measure for Jump-Diffusion Term Structure Models," Research Paper Series 198, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  13. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 1-22, March. [Downloadable!] (restricted)
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  14. 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. [Downloadable!]
  15. Eckhard Platen & Wolfgang Runggaldier, 2004. "A Benchmark Approach to Filtering in Finance," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 79-105, March. [Downloadable!] (restricted)
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  16. Eckhard Platen, 2004. "Capital Asset Pricing for Markets with Intensity Based Jumps," Research Paper Series 143, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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