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Diversified Portfolios with Jumps in a Benchmark Framework

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  • Eckhard Platen

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Abstract

This paper considers diversified portfolios in a sequence of jump diffusion market models. Conditions for the approximation of the growth optimal portfolio (GOP) by diversified portfolios are provided. Under realistic assumptions, it is shown that diversified portfolios approximate the GOP without requiring any major model specifications. This provides a basis for systematic use of diversified stock indices as proxies for the GOP in derivative pricing, risk management and portfolio optimization. Copyright Springer Science + Business Media, Inc. 2004

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File URL: http://hdl.handle.net/10.1007/s10690-005-4253-8
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Bibliographic Info

Article provided by Springer in its journal Asia-Pacific Financial Markets.

Volume (Year): 11 (2004)
Issue (Month): 1 (March)
Pages: 1-22

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Handle: RePEc:kap:apfinm:v:11:y:2004:i:1:p:1-22

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Web page: http://springerlink.metapress.com/link.asp?id=102851

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Keywords: benchmark model; diversified portfolio; growth optimal portfolio;

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References

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  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.
  2. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
  3. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  4. Norbert Hofmann & Eckhard Platen, 2000. "Approximating Large Diversified Portfolios," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 77-88.
  5. I. Bajeux-Besnainou & R. Portait, 1997. "The numeraire portfolio: a new perspective on financial theory," European Journal of Finance, Taylor and Francis Journals, vol. 3(4), pages 291-309.
  6. 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.
  7. 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.
  8. David Heath & Eckhard Platen, 2002. "Consistent pricing and hedging for a modified constant elasticity of variance model," Quantitative Finance, Taylor and Francis Journals, vol. 2(6), pages 459-467.
  9. Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  11. Eckhard Platen, 2002. "Benchmark Model with Intensity Based Jumps," Research Paper Series 81, Quantitative Finance Research Centre, University of Technology, Sydney.
  12. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
  13. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  14. David Heath & Eckhard Platen, 2003. "Pricing of Index Options Under a Minimal Market Model with Lognormal Scaling," Research Paper Series 101, Quantitative Finance Research Centre, University of Technology, Sydney.
  15. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-52.
  16. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  17. L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176.
  18. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  19. Eckhard Platen, 2003. "A Benchmark Framework for Risk Management," Research Paper Series 113, Quantitative Finance Research Centre, University of Technology, Sydney.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. Eckhard Platen & Wolfgang Runggaldier, 2002. "A Benchmark Approach to Filtering in Finance," Research Paper Series 77, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Francesca Biagini & Alessandra Cretarola & Eckhard Platen, 2012. "Local Risk-Minimization under the Benchmark Approach," Research Paper Series 319, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Eckhard Platen, 2009. "A Benchmark Approach to Investing and Pricing," Research Paper Series 253, Quantitative Finance Research Centre, University of Technology, Sydney.
  6. Eckhard Platen & Wolfgang Runggaldier, 2007. "A Benchmark Approach to Portfolio Optimization under Partial Information," Research Paper Series 191, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor and Francis Journals, vol. 13(1), pages 19-38.
  8. Ke Du & Eckhard Platen, 2011. "Three-Benchmarked Risk Minimization for Jump Diffusion Markets," Research Paper Series 296, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.
  10. Eckhard Platen & Jason West & Wolfgang Breymann, 2004. "An Intraday Empirical Analysis of Electricity Price Behaviour," Research Paper Series 140, Quantitative Finance Research Centre, University of Technology, Sydney.
  11. 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.
  12. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
  13. Eckhard Platen, 2004. "Capital Asset Pricing for Markets with Intensity Based Jumps," Research Paper Series 143, Quantitative Finance Research Centre, University of Technology, Sydney.
  14. Eckhard Platen, 2006. "On the Pricing and Hedging of Long Dated Zero Coupon Bonds," Research Paper Series 185, Quantitative Finance Research Centre, University of Technology, Sydney.

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