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Consistent Pricing and Hedging for a Modified Constant Elasticity of Variance Model

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Abstract

This paper considers a modification of the well-known constant elasticity of variance model where it is used to model the growth optimal portfolio. It is shown taht, for this application, there is no equivalent risk neutral pricing methodology fails. However, a consistent pricing and hedging framework can be established by application of the benchmark approach. Perfect hedging strategies can be constructed for European style contingent claims, where the underlying risky asset is the growth optimal portfolio. In this framework, fair prices for contingent claims are the minimal prices that permit perfect replication of the claims. Numerical examples show that these prices may differ significantly from the corresponding "risk neutral" prices. In cases where these prices are different, arbitrage amounts can be generated.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp78.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 78.

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Date of creation: 01 May 2002
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Handle: RePEc:uts:rpaper:78

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Keywords: risk neutral pricing; benchmark model; constant elasticity of variance; fair pricing;

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References

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  1. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  2. Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
  4. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-19, March.
  5. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, July.
  6. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
  8. Beckers, Stan, 1980. " The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-73, June.
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Cited by:
  1. Eckhard Platen & Wolfgang Runggaldier, 2002. "A Benchmark Approach to Filtering in Finance," Research Paper Series 77, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. David Heath & Eckhard Platen, 2006. "Local volatility function models under a benchmark approach," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 197-206.
  3. Eckhard Platen, 2004. "Capital Asset Pricing for Markets with Intensity Based Jumps," Research Paper Series 143, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 1-22, March.
  5. Baldeaux Jan & Ignatieva Katja & Platen Eckhard, 2014. "A tractable model for indices approximating the growth optimal portfolio," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(1), pages 1-21, February.
  6. Hardy Hulley & Eckhard Platen, 2007. "Laplace Transform Identities for Diffusions, with Applications to Rebates and Barrier Options," Research Paper Series 203, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Eckhard Platen, 2003. "A Benchmark Framework for Risk Management," Research Paper Series 113, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. T. Marquardt & Eckhard Platen & S. Jaschke, 2008. "Valuing Guaranteed Minimum Death Benefit Options in Variable Annuities Under a Benchmark Approach," Research Paper Series 221, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. Johannes Ruf, 2010. "Hedging under arbitrage," Papers 1003.4797, arXiv.org, revised May 2011.

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