IDEAS home Printed from https://ideas.repec.org/a/eee/ecofin/v76y2025ics1062940825000129.html
   My bibliography  Save this article

Multi-step double barrier options under time-varying interest rates

Author

Listed:
  • Lee, Hangsuck
  • Kye, Yisub
  • Kong, Byungdoo
  • Song, Seongjoo

Abstract

Double barrier options are popular in the over-the-counter market due to their flexible investment strategies, opportunities to capitalize on volatility, and potential for increased leverage and more significant price movements, enhancing possible payoffs by incorporating two barrier levels. Multi-step double barrier options are particularly useful since they allow investors to set the barrier levels in a flexible manner while they are computationally efficient due to the explicit pricing formulas. In our study, we propose a method for pricing multi-step double barrier options under time-varying interest rates, acknowledging the potential unrealistic nature of employing a constant interest rate in economic scenarios marked by frequent adjustments in central bank monetary policies, such as during the COVID-19 pandemic. The method we employ to introduce a time-varying feature to the interest rate entails incorporating random jumps at various time points as needed. Our setup allows us to incorporate jumps not only in the interest rate dynamics but also in the asset price, so we can utilize jumps to more comprehensively depict the random nature of underlying price movement.

Suggested Citation

  • Lee, Hangsuck & Kye, Yisub & Kong, Byungdoo & Song, Seongjoo, 2025. "Multi-step double barrier options under time-varying interest rates," The North American Journal of Economics and Finance, Elsevier, vol. 76(C).
    • Handle: RePEc:eee:ecofin:v:76:y:2025:i:c:s1062940825000129
    DOI: 10.1016/j.najef.2025.102372
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1062940825000129
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.najef.2025.102372?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ben S. Bernanke & Kenneth N. Kuttner, 2005. "What Explains the Stock Market's Reaction to Federal Reserve Policy?," Journal of Finance, American Finance Association, vol. 60(3), pages 1221-1257, June.
    2. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    3. Bento J. Lobo, 2002. "Interest Rate Surprises and Stock Prices," The Financial Review, Eastern Finance Association, vol. 37(1), pages 73-91, February.
    4. Ning Cai & S. G. Kou, 2011. "Option Pricing Under a Mixed-Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 57(11), pages 2067-2081, November.
    5. Hangsuck Lee & Gaeun Lee & Seongjoo Song, 2022. "Multi‐step reflection principle and barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(4), pages 692-721, April.
    6. Kontonikas, Alexandros & MacDonald, Ronald & Saggu, Aman, 2013. "Stock market reaction to fed funds rate surprises: State dependence and the financial crisis," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4025-4037.
    7. Hangsuck Lee & Seongjoo Song & Gaeun Lee, 2023. "Insurance guaranty premiums and exchange options," Mathematics and Financial Economics, Springer, volume 17, number 3, October.
    8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Clara Vega, 2003. "Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange," American Economic Review, American Economic Association, vol. 93(1), pages 38-62, March.
    9. Tristan Guillaume, 2010. "Step double barrier options," Post-Print hal-00924266, HAL.
    10. Hangsuck Lee & Hongjun Ha & Minha Lee, 2022. "Piecewise linear double barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(1), pages 125-151, January.
    11. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    12. Chuliá, Helena & Martens, Martin & Dijk, Dick van, 2010. "Asymmetric effects of federal funds target rate changes on S&P100 stock returns, volatilities and correlations," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 834-839, April.
    13. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    14. repec:bla:jfinan:v:59:y:2004:i:1:p:227-260 is not listed on IDEAS
    15. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
    16. Thorbecke, Willem, 1997. "On Stock Market Returns and Monetary Policy," Journal of Finance, American Finance Association, vol. 52(2), pages 635-654, June.
    17. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    18. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    19. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
    20. Peng Jin, 2017. "Brownian Motion with Singular Time-Dependent Drift," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1499-1538, December.
    21. Lee, Hangsuck & Jeong, Himchan & Lee, Minha, 2022. "Multi-step double barrier options," Finance Research Letters, Elsevier, vol. 47(PA).
    22. Lee, Hangsuck & Ko, Bangwon & Lee, Minha, 2023. "The pricing and static hedging of multi-step double barrier options," Finance Research Letters, Elsevier, vol. 55(PA).
    23. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    24. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298, October.
    25. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double‐Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378, October.
    26. Cho H. Hui, 1997. "Time‐dependent barrier option values," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 17(6), pages 667-688, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Buckley, Winston & Long, Hongwei & Marshall, Mario, 2016. "Numerical approximations of optimal portfolios in mispriced asymmetric Lévy markets," European Journal of Operational Research, Elsevier, vol. 252(2), pages 676-686.
    2. Markus Leippold & Nikola Vasiljević, 2020. "Option-Implied Intrahorizon Value at Risk," Management Science, INFORMS, vol. 66(1), pages 397-414, January.
    3. Lee, Hangsuck & Jeong, Himchan & Lee, Minha, 2022. "Multi-step double barrier options," Finance Research Letters, Elsevier, vol. 47(PA).
    4. Lee, Hangsuck & Ha, Hongjun & Kong, Byungdoo & Lee, Minha, 2023. "Pricing multi-step double barrier options by the efficient non-crossing probability," Finance Research Letters, Elsevier, vol. 54(C).
    5. Michael C. Fu & Bingqing Li & Guozhen Li & Rongwen Wu, 2017. "Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions," Management Science, INFORMS, vol. 63(11), pages 3961-3977, November.
    6. Lee, Hangsuck & Lee, Gaeun & Song, Seongjoo, 2023. "Min–max multi-step barrier options and their variants," The North American Journal of Economics and Finance, Elsevier, vol. 67(C).
    7. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384, July.
    8. Li, Xin, 2023. "Generalized two-barrier proportional step options," Finance Research Letters, Elsevier, vol. 51(C).
    9. Cao, Wenbin & Guernsey, Scott B. & Linn, Scott C., 2018. "Evidence of infinite and finite jump processes in commodity futures prices: Crude oil and natural gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 629-641.
    10. Lian, Guanghua & Zhu, Song-Ping & Elliott, Robert J. & Cui, Zhenyu, 2017. "Semi-analytical valuation for discrete barrier options under time-dependent Lévy processes," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 167-183.
    11. Lee, Hangsuck & Choi, Yang Ho & Lee, Gaeun, 2022. "Multi-step barrier products and static hedging," The North American Journal of Economics and Finance, Elsevier, vol. 61(C).
    12. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2019. "Sinh-Acceleration: Efficient Evaluation Of Probability Distributions, Option Pricing, And Monte Carlo Simulations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-49, May.
    13. Nkwoma, Inekwe John, 2017. "Futures-Based Measures Of Monetary Policy And Jump Risk," Macroeconomic Dynamics, Cambridge University Press, vol. 21(2), pages 384-405, March.
    14. Walter Farkas & Ludovic Mathys, 2020. "Geometric Step Options with Jumps. Parity Relations, PIDEs, and Semi-Analytical Pricing," Papers 2002.09911, arXiv.org.
    15. Lee, Hangsuck & Ko, Bangwon & Lee, Minha, 2023. "The pricing and static hedging of multi-step double barrier options," Finance Research Letters, Elsevier, vol. 55(PA).
    16. Lee, Hangsuck & Lee, Minha & Ha, Hongjun, 2025. "Multi-piecewise linear double barrier options," Finance Research Letters, Elsevier, vol. 75(C).
    17. Tim Leung & Marco Santoli, 2014. "Accounting for earnings announcements in the pricing of equity options," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 1-46.
    18. Kam F. Chan & Philip Gray, 2018. "Volatility jumps and macroeconomic news announcements," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(8), pages 881-897, August.
    19. Weng, Chengguo, 2013. "Constant proportion portfolio insurance under a regime switching exponential Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 508-521.
    20. Jun, Doobae & Ku, Hyejin, 2015. "Static hedging of chained-type barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 317-327.

    More about this item

    Keywords

    Time-varying interest rate; Brownian motion; Piecewise constant drift; Multi-step double barrier; Esscher transform; Binomial jumps;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecofin:v:76:y:2025:i:c:s1062940825000129. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/620163 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.