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Pricing Multi-Asset Options with an External Barrier

Author

Listed:
  • Yue-Kuen Kwok

    (Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

  • Lixin Wu

    (Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

  • Hong Yu

    (Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

Abstract

An external barrier of an option contract is a stochastic variable which determines whether the option is knocked in or out when the value of the variable is above or below some predetermined level, but itself is not the price of an asset which underlies the option. In this paper, we present analytic formulation for the valuation of European options on one or multiple assets with single external barrier, where the barrier level can be exponential. As the domain of the problem becomes semi-infinite due to the presence of the external barrier, we employ the method of images to find the Green function of the governing differential equation. An efficient and accurate fractional step finite difference scheme is proposed for the numerical valuation of these barrier options.

Suggested Citation

  • Yue-Kuen Kwok & Lixin Wu & Hong Yu, 1998. "Pricing Multi-Asset Options with an External Barrier," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 523-541.
    • Handle: RePEc:wsi:ijtafx:v:01:y:1998:i:04:n:s021902499800028x
    DOI: 10.1142/S021902499800028X
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    Cited by:

    1. Donghyun Kim & Ji-Hun Yoon, 2023. "Analytic Method for Pricing Vulnerable External Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1561-1591, April.
    2. Yang, Nian & Chen, Nan & Liu, Yanchu & Wan, Xiangwei, 2017. "Approximate arbitrage-free option pricing under the SABR model," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 198-214.
    3. Kim, Jerim & Kim, Jeongsim & Joo Yoo, Hyun & Kim, Bara, 2015. "Pricing external barrier options in a regime-switching model," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 123-143.
    4. Guangming Xue & Bin Qin & Guohe Deng, 2018. "Valuation on an Outside-Reset Option with Multiple Resettable Levels and Dates," Complexity, Hindawi, vol. 2018, pages 1-13, April.

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