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Johnson binomial trees

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  • Jean-Guy Simonato

Abstract

Rubinstein developed a binomial lattice technique for pricing European and American derivatives in the context of skewed and leptokurtic asset return distributions. A drawback of this approach is the limited set of skewness and kurtosis pairs for which valid stock return distributions are possible. A solution to this problem is proposed here by extending Rubinstein's Edgeworth tree idea to the case of the Johnson system of distributions which is capable of accommodating all possible skewness and kurtosis pairs. Numerical examples showing the performance of the Johnson tree to approximate the prices of European and American options in Merton's jump diffusion framework and Duan's GARCH framework are examined.

Suggested Citation

  • Jean-Guy Simonato, 2011. "Johnson binomial trees," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1165-1176.
  • Handle: RePEc:taf:quantf:v:11:y:2011:i:8:p:1165-1176
    DOI: 10.1080/14697680902950821
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    References listed on IDEAS

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    1. Andrew Ziogas & Carl Chiarella, 2004. "Pricing American Options on Jump-Diffusion Processes using Fourier-Hermite Series Expansions," Computing in Economics and Finance 2004 177, Society for Computational Economics.
    2. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
    3. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31 World Scientific Publishing Co. Pte. Ltd..
    4. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    5. Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1689-1718, November.
    6. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
    7. Jin‐Chuan Duan & Geneviève Gauthier & Caroline Sasseville & Jean‐Guy Simonato, 2003. "Approximating American option prices in the GARCH framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(10), pages 915-929, October.
    8. Jin-Chuan Duan & Jean-Guy Simonato, 1998. "Empirical Martingale Simulation for Asset Prices," Management Science, INFORMS, vol. 44(9), pages 1218-1233, September.
    9. Peter Ritchken & L. Sankarasubramanian & Anand M. Vijh, 1993. "The Valuation of Path Dependent Contracts on the Average," Management Science, INFORMS, vol. 39(10), pages 1202-1213, October.
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    Cited by:

    1. Marcellino Gaudenzi & Alice Spangaro & Patrizia Stucchi, 2017. "Efficient European and American option pricing under a jump-diffusion process," Papers 1712.08137, arXiv.org.

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