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Risk premia and financial modelling without measure transformation

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  • Platen, Eckhard

Abstract

This paper describes a financial market modelling framework that exploits the notion of a deflator . The denominations of the deflator measured in units of primary assets form a minimal set of basic financial quantities that completely specify the overall market dynamics, where deflated asset prices appear as martingales. A specific form for the risk premia is obtained as a natural consequence of the approach. Contingent claim prices are computed under the real world measure both in the case of complete and incomplete markets avoiding the use of an equivalent risk neutral measure transformation.

Suggested Citation

  • Platen, Eckhard, 2000. "Risk premia and financial modelling without measure transformation," SFB 373 Discussion Papers 2000,92, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200092
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    References listed on IDEAS

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    1. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
    2. Eckhard Platen, 1999. "A Minimal Share Market Model with Stochastic Volatility," Research Paper Series 21, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. 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, April.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. David Heath & Eckhard Platen, 2001. "Pricing and Hedging of Index Derivatives under an Alternative Asset Price Model with Endogenous Stochastic Volatility," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 10, pages 117-126, World Scientific Publishing Co. Pte. Ltd..
    6. Eckhard Platen, 1999. "Axiomatic principles for a market model," Published Paper Series 1999-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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    Citations

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    Cited by:

    1. Song Xi Chen & Wolfgang Härdle & Ming Li, 2003. "An empirical likelihood goodness‐of‐fit test for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 663-678, August.
    2. Wolfgang Hardle & Torsten Kleinow & Alexander Korostelev & Camille Logeay & Eckhard Platen, 2008. "Semiparametric diffusion estimation and application to a stock market index," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 81-92.
    3. Rei[ss], Oliver & Schoenmakers, John & Schweizer, Martin, 2007. "From structural assumptions to a link between assets and interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 593-612, February.
    4. David Heath & Eckhard Platen, 2001. "Perfect Hedging of Index Derivatives Under a Locally Arbitrage Free Minimal Market Model," Research Paper Series 61, Quantitative Finance Research Centre, University of Technology, Sydney.

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    More about this item

    Keywords

    financial market modelling; deflator; risk premium; contingent claim pricing; incomplete market;
    All these keywords.

    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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