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Analytical valuation of a general form of barrier option with stochastic interest rate and jumps

Author

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  • Tristan Guillaume

    (CY Cergy Paris Université)

Abstract

This article provides exact valuation formulae for barrier options with a stochastic, outside and window barrier, in a model allowing for stochastic interest rate and jumps in the underlying asset. The case of a best-of option with the same barrier and model specifications is also covered. Formulae in the classical, more restrictive Black–Scholes environment are derived too. These analytical results are numerically implemented and the obtained values are compared with Monte Carlo approximations.

Suggested Citation

  • Tristan Guillaume, 2025. "Analytical valuation of a general form of barrier option with stochastic interest rate and jumps," Review of Derivatives Research, Springer, vol. 28(2), pages 1-44, July.
    • Handle: RePEc:kap:revdev:v:28:y:2025:i:2:d:10.1007_s11147-025-09215-6
    DOI: 10.1007/s11147-025-09215-6
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    References listed on IDEAS

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    1. Peter Carr & Andrey Itkin & Dmitry Muravey, 2020. "Semi-closed form prices of barrier options in the time-dependent CEV and CIR models," Papers 2005.05459, arXiv.org.
    2. 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.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Tianqi Zhang & Bingqing Li, 2022. "Pricing double-barrier option with processes depending on various states of the economy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(23), pages 8296-8309, October.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. Bakshi, Gurdip & Crosby, John & Gao, Xiaohui & Hansen, Jorge W., 2023. "Treasury option returns and models with unspanned risks," Journal of Financial Economics, Elsevier, vol. 150(3).
    7. Andrey Itkin & Dmitry Muravey, 2020. "Semi-closed form prices of barrier options in the Hull-White model," Papers 2004.09591, arXiv.org, revised Sep 2020.
    8. Tristan Guillaume, 2022. "Closed form valuation of barrier options with stochastic barriers," Annals of Operations Research, Springer, vol. 313(2), pages 1021-1050, June.
    9. Stulz, ReneM., 1982. "Options on the minimum or the maximum of two risky assets : Analysis and applications," Journal of Financial Economics, Elsevier, vol. 10(2), pages 161-185, July.
    10. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, François, 2008. "Pricing derivatives with barriers in a stochastic interest rate environment," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2903-2938, September.
    11. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298, October.
    12. Oleg Kudryavtsev & Sergei Levendorskiǐ, 2009. "Fast and accurate pricing of barrier options under Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 531-562, September.
    13. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    14. Grant Armstrong, 2001. "Valuation formulae for window barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 197-208.
    15. Damir Filipović & Martin Larsson & Anders B. Trolle, 2017. "Linear-Rational Term Structure Models," Journal of Finance, American Finance Association, vol. 72(2), pages 655-704, April.
    16. Marianito R. Rodrigo, 2020. "Pricing of Barrier Options on Underlying Assets with Jump-Diffusion Dynamics: A Mellin Transform Approach," Mathematics, MDPI, vol. 8(8), pages 1-20, August.
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    More about this item

    Keywords

    Barrier option; Multi-asset option; Stochastic yield curve; Jump-diffusion; Best-of option; Stochastic barrier; Outside barrier; Window barrier;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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