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On option pricing in binomial market with transaction costs

Author

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  • Alexander Melnikov
  • Yury Petrachenko

Abstract

Option replication is studied in a discrete-time framework with proportional transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option-pricing model to cover the case of proportional transaction costs for one risky asset with different interest rates on bank credit and deposit. Contingent claims are supposed to be 2-dimensional random variables. Explicit formulas for self-financing strategies are obtained for this case. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Alexander Melnikov & Yury Petrachenko, 2005. "On option pricing in binomial market with transaction costs," Finance and Stochastics, Springer, vol. 9(1), pages 141-149, January.
    • Handle: RePEc:spr:finsto:v:9:y:2005:i:1:p:141-149
    DOI: 10.1007/s00780-004-0134-7
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    Citations

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    Cited by:

    1. Barbara Trivellato, 2009. "Replication and shortfall risk in a binomial model with transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 1-26, March.
    2. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, January.
    3. Tokarz, Krzysztof & Zastawniak, Tomasz, 2006. "American contingent claims under small proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 65-85, December.
    4. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2021. "Market Complete Option Valuation using a Jarrow-Rudd Pricing Tree with Skewness and Kurtosis," Papers 2106.09128, arXiv.org.
    5. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    6. Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).

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