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A Generalization of the Brennan-Rubinstein Approach for the Pricing of Derivatives

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  • António Câmara

    (Department of Accounting and Finance, Strathclyde University)

Abstract

This paper derives preference-free option pricing equations in a discrete time economy where asset returns have continuous distributions. There is a representative agent who has risk preferences with an exponential representation. Aggregate wealth and the underlying asset price have transformed normal distributions which may or may not belong to the same family of distributions. Those pricing results are particularly valuable (a) to show new sufficient conditions for existing risk-neutral option pricing equations (e.g., the Black-Scholes model), and (b) to obtain new analytical solutions for the price of European-style contingent claims when the underlying asset has a transformed normal distribution (e.g., a negatively skew lognormal distribution). Copyright (c) 2003 by the American Finance Association.

Suggested Citation

  • António Câmara, 2003. "A Generalization of the Brennan-Rubinstein Approach for the Pricing of Derivatives," Journal of Finance, American Finance Association, vol. 58(2), pages 805-820, April.
  • Handle: RePEc:bla:jfinan:v:58:y:2003:i:2:p:805-820
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    Cited by:

    1. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers 2012-50, Department of Economics and Business Economics, Aarhus University.
    2. Monfort, Alain & Pegoraro, Fulvio, 2012. "Asset pricing with Second-Order Esscher Transforms," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1678-1687.
    3. Schröder, Michael & Lüders, Erik, 2004. "Modeling Asset Returns: A Comparison of Theoretical and Empirical Models," ZEW Discussion Papers 04-19 [rev.], ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    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. Choi, Pilsun & Min, Insik & Park, Keehwan, 2012. "SU-ΔCoVaR," Economics Letters, Elsevier, vol. 115(2), pages 218-220.
    6. Luiz Vitiello & Ser-Huang Poon, 2014. "Non-monotonic pricing kernel and an extended class of mixture of distributions for option pricing," Review of Derivatives Research, Springer, vol. 17(2), pages 241-259, July.
    7. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    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.

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