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

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.qfrc.uts.edu.au/research/research_papers/rp78.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 78.

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Length: 19 pages
Date of creation: 01 May 2002
Date of revision:
Publication status: Published as: Heath, D. and Platen, E., 2002, "Consistent Pricing and Hedging for a Modified Constant Elasticity of Variance Model", Quantitative Finance, 2(6), 459-467.
Handle: RePEc:uts:rpaper:78
Contact details of provider: Postal: PO Box 123, Broadway, NSW 2007, Australia
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Web page: http://www.qfrc.uts.edu.au/

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  1. 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.
  2. Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. 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.
  4. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
  5. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  6. 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.
  7. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  8. 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.
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