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Barrier Option Pricing By Branching Processes

Author

Listed:
  • GEORGI K. MITOV

    (Institute of Mathematics and Informatics, Bulgarian Academy of Science, "Acad. G. Bonchev" Str., Bl. 8, 1113, Sofia Bulgaria;
    FinAnalytica Inc., Sofia Bulgaria)

  • SVETLOZAR T. RACHEV

    (School of Economics and Business Engineering, University of Karlsruhe and KIT, Kollegium am Schloss, Bau II, 20.12, R210, Postfach 6980, D-76128, Karlsruhe, Germany;
    Department of Statistics and Applied Probability, University of California, Santa Barbara, USA;
    FinAnalytica Inc., USA)

  • YOUNG SHIN KIM

    (Department of Statistics, Econometrics and Mathematical Finance, School of Economics and Business Engineering, University of Karlsruhe, Germany;
    KIT, Kollegium am Schloss, Bau II, 20.12, R210, Postfach 6980, D-76128, Karlsruhe, Germany)

  • FRANK J. FABOZZI

    (Yale School of Management, 135 Prospect Street, Box 208200, New Haven, CT 06520-8200, USA)

Abstract

This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is performed using market prices of standard call options. Our results show that the prices of barrier options that are priced with the BPRE model deviate significantly from those modeled assuming a lognormal process, despite the fact that for standard options, the corresponding differences between the two models are relatively small.

Suggested Citation

  • Georgi K. Mitov & Svetlozar T. Rachev & Young Shin Kim & Frank J. Fabozzi, 2009. "Barrier Option Pricing By Branching Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1055-1073.
    • Handle: RePEc:wsi:ijtafx:v:12:y:2009:i:07:n:s0219024909005555
    DOI: 10.1142/S0219024909005555
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    References listed on IDEAS

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    1. Thomas W Epps, 2007. "Pricing Derivative Securities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6243, February.
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    Cited by:

    1. Ali Saeb, 2022. "Stock Prices as Janardan Galton Watson Process," Papers 2208.08496, arXiv.org.

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