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Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models

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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 class of incomplete financial market models with security price processes that exhibit intensity based jumps. The benchmark or numeraire is chosen to be the growth optimal portfolio. Portfolio values, when expressed in units of the benchmark, are local martingales. In general, an equivalent risk neutral martingale measure need not exist in the proposed framework. Benchmarked fair derivative prices are defined as conditional expectations of future benchmarked prices under the real world probability measure. This concept of fair pricing generalizes classical risk neutral pricing. The pricing under incompleteness is modeled by the choice of the market prices for risk. The hedging is performed under minimization of profit and loss fluctuations.

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Publisher Info
Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 110.

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Date of creation: 03 Oct 2003
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Handle: RePEc:uts:rpaper:110

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Related research
Keywords: benchmark model; jump diffusions; incomplete market; growth optimal portfolio; fair pricing; hedge error minimization;

Other versions of this item:

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

This paper has been announced in the following NEP Reports:

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. David Heath & Eckhard Platen, 2002. "Consistent Pricing and Hedging for a Modified Constant Elasticity of Variance Model," Research Paper Series 78, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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  2. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Blackwell Publishing, vol. 11(4), pages 385-413. [Downloadable!] (restricted)
  3. N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B 209, University of Bonn, Germany.
  4. 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, December. [Downloadable!] (restricted)
  5. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July. [Downloadable!] (restricted)
  6. Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
    Other versions:
  7. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  8. Eckhard Platen, 2002. "Benchmark Model with Intensity Based Jumps," Research Paper Series 81, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  9. 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. [Downloadable!]
Full references

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. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
  2. 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)
  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. [Downloadable!]
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