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Pricing external barrier options in a regime-switching model

Author

Listed:
  • Kim, Jerim
  • Kim, Jeongsim
  • Joo Yoo, Hyun
  • Kim, Bara

Abstract

External barrier options are two-asset options where the payoff is defined on one asset and the barrier is defined on another asset. In this paper, we derive the Laplace transforms of the prices and deltas for the external single and double barrier options where the underlying asset prices follow a regime-switching model with finite regimes. The derivation is made possible because we can obtain the joint Laplace transform of the first passage time of one asset value and the value of the other asset. Numerical inversion of the Laplace transforms is used to calculate the prices of external barrier options.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:dyncon:v:53:y:2015:i:c:p:123-143
    DOI: 10.1016/j.jedc.2015.02.007
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    References listed on IDEAS

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    1. Zhengjun Jiang & Martijn Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Finance and Stochastics, Springer, vol. 12(3), pages 331-355, July.
    2. P. Carr, 1995. "Two extensions to barrier option valuation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 173-209.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Carl Chiarella & Boda Kang & Gunter H. Meyer, 2010. "The Evaluation Of Barrier Option Prices Under Stochastic Volatility," Research Paper Series 266, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Z. Jiang & M. R. Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Papers 0803.2302, arXiv.org.
    6. Hoi Ying Wong & Yue-Kuen Kwok, 2003. "Multi-asset barrier options and occupation time derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(3), pages 245-266.
    7. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    8. 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.
    9. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298, October.
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    Citations

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    Cited by:

    1. Zhang, Xiaoyuan & Zhang, Tianqi, 2022. "Barrier option pricing under a Markov Regime switching diffusion model," The Quarterly Review of Economics and Finance, Elsevier, vol. 86(C), pages 273-280.
    2. 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.
    3. Zhang, Xiaoyuan & Zhang, Tianqi, 2023. "On pricing double-barrier options with Markov regime switching," Finance Research Letters, Elsevier, vol. 51(C).
    4. Roy Cerqueti, 2022. "A new concept of reliability system and applications in finance," Annals of Operations Research, Springer, vol. 312(1), pages 45-64, May.
    5. Gao, Yin & Tian, Miao, 2024. "Pricing problem and sensitivity analysis of knock-in external barrier options based on uncertain stock model," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    6. Gzyl, H. & Milev, M. & Tagliani, A., 2017. "Discontinuous payoff option pricing by Mellin transform: A probabilistic approach," Finance Research Letters, Elsevier, vol. 20(C), pages 281-288.

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    More about this item

    Keywords

    External barrier option; Regime-switching; First passage time; Sylvester matrix equation; Laplace transform; Option price;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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