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Risk-Neutral Parameter Shifts and Derivatives Pricing in Discrete Time

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  • MARK SCHRODER
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    Abstract

    We obtain a large class of discrete-time risk-neutral valuation relationships, or "preference-free" derivatives pricing models, by imposing a simple restriction on the state-price density process. The risk-neutral stock-return and forward-rate dynamics are obtained by changing only a location parameter, which can be determined independent of the preference and true location parameters. The Gaussian models of Rubinstein (1976) , Brennan (1979) , and Câmera (2003) , and the gamma model of Heston (1993) are all special cases. The model provides simple relationships between expected returns and state-price density parameters analogous to the diffusion case. Copyright 2004 by The American Finance Association.

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    Bibliographic Info

    Article provided by American Finance Association in its journal The Journal of Finance.

    Volume (Year): 59 (2004)
    Issue (Month): 5 (October)
    Pages: 2375-2402

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    Handle: RePEc:bla:jfinan:v:59:y:2004:i:5:p:2375-2402

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    Cited by:
    1. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2010. "Option Valuation with Conditional Heteroskedasticity and Nonnormality," Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2139-2183.
    2. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, Elsevier, vol. 90(3), pages 272-297, December.
    3. Guenter Franke & James Huang & Richard Stapleton, 2006. "Two-dimensional risk-neutral valuation relationships for the pricing of options," Review of Derivatives Research, Springer, vol. 9(3), pages 213-237, November.
    4. Bertram Düring & Erik Lüders, 2005. "Option Prices Under Generalized Pricing Kernels," Review of Derivatives Research, Springer, vol. 8(2), pages 97-123, August.
    5. Bertram Düring, 2008. "Asset Pricing Under Information with Stochastic Volatility," CoFE Discussion Paper 08-04, Center of Finance and Econometrics, University of Konstanz.
    6. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers 2012-50, School of Economics and Management, University of Aarhus.
    7. Badescu, Alex & Elliott, Robert J. & Siu, Tak Kuen, 2009. "Esscher transforms and consumption-based models," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 337-347, December.
    8. Câmara, António & Popova, Ivilina & Simkins, Betty, 2012. "A comparative study of the probability of default for global financial firms," Journal of Banking & Finance, Elsevier, vol. 36(3), pages 717-732.
    9. John, Kose & Reisz, Alexander S., 2010. "Temporal resolution of uncertainty, disclosure policy, and corporate debt yields," Journal of Corporate Finance, Elsevier, Elsevier, vol. 16(5), pages 655-678, December.

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