IDEAS home Printed from https://ideas.repec.org/a/gam/jecomi/v12y2024i3p73-d1359993.html

Discretely Distributed Scheduled Jumps and Interest Rate Derivatives: Pricing in the Context of Central Bank Actions

Author

Listed:
  • Allan Jonathan da Silva

    (Coordination of Mathematical and Computational Methods, National Laboratory for Scientific Computing (LNCC), Petrópolis 25651-075, RJ, Brazil
    Department of Production Engineering, Federal Center for Technological Education Celso Suckow da Fonseca (Cefet/RJ), Itaguaí 23812-101, RJ, Brazil)

  • Jack Baczynski

    (Coordination of Mathematical and Computational Methods, National Laboratory for Scientific Computing (LNCC), Petrópolis 25651-075, RJ, Brazil)

Abstract

Interest rate dynamics are influenced by various economic factors, and central bank meetings play a crucial role concerning this subject matter. This study introduces a novel approach to modeling interest rates, focusing on the impact of central banks’ scheduled interventions and their implications for pricing bonds and path-dependent derivatives. We utilize a modified Skellam probability distribution to address the discrete nature of scheduled interest rate jumps and combine them with affine jump-diffusions (AJDs) in order to realistically represent interest rates. We name this class the AJD–Skellam models. Within this class, we provide closed-form formulas for the characteristic functions of a still broad class of interest rate models. The AJD–Skellam models are well-suited for using the interest rate version of the Fourier-cosine series (COS) method for fast and efficient interest rate derivative pricing. Our methodology incorporates this method. The results obtained in the paper demonstrate enhanced accuracy in capturing market behaviors and in pricing interest rate products compared to traditional diffusion models with random jumps. Furthermore, we highlight the applicability of the model to risk management and its potential for broader financial analysis.

Suggested Citation

  • Allan Jonathan da Silva & Jack Baczynski, 2024. "Discretely Distributed Scheduled Jumps and Interest Rate Derivatives: Pricing in the Context of Central Bank Actions," Economies, MDPI, vol. 12(3), pages 1-29, March.
    • Handle: RePEc:gam:jecomi:v:12:y:2024:i:3:p:73-:d:1359993
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7099/12/3/73/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7099/12/3/73/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Lin, Shih-Kuei & Wang, Shin-Yun & Chen, Carl R. & Xu, Lian-Wen, 2017. "Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 359-373.
    3. Gongyan Yang & Hongzhong Liu, 2016. "Financial Development, Interest Rate Liberalization, and Macroeconomic Volatility," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 52(4), pages 991-1001, April.
    4. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alessandro Calvia & Marzia De Donno & Chiara Guardasoni & Simona Sanfelici, 2025. "Short-rate models with stochastic discontinuities: a PDE approach," Papers 2510.04289, arXiv.org, revised Jan 2026.

    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. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6, July-Dece.
    2. Lin, Shih-Kuei & Wang, Shin-Yun & Chen, Carl R. & Xu, Lian-Wen, 2017. "Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 359-373.
    3. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    4. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    5. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2005, January-A.
    6. Etienne Vaccaro-Grange, 2025. "Quantitative easing, tightening, and the term premium channel in the Euro Area," Empirical Economics, Springer, vol. 69(6), pages 3089-3125, December.
    7. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    8. Álvarez Echeverría Francisco & López Sarabia Pablo & Venegas Martínez Francisco, 2012. "Valuación financiera de proyectos de inversión en nuevas tecnologías con opciones reales," Contaduría y Administración, Accounting and Management, vol. 57(3), pages 115-145, julio-sep.
    9. Dufrénot, Gilles & Gente, Karine & Monsia, Frédia, 2016. "Macroeconomic imbalances, financial stress and fiscal vulnerability in the euro area before the debt crises: A market view," Journal of International Money and Finance, Elsevier, vol. 67(C), pages 123-146.
    10. Matsumura, Marco & Moreira, Ajax & Vicente, José, 2011. "Forecasting the yield curve with linear factor models," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 237-243.
    11. I‐Doun Kuo & Yueh‐Neng Lin, 2009. "Empirical performance of multifactor term structure models for pricing and hedging Eurodollar futures options," Review of Financial Economics, John Wiley & Sons, vol. 18(1), pages 23-32, January.
    12. Gluzberg, Victor E. & Katz, Yuri A., 2019. "Planetary boundaries of consumption growth: Declining social discount rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 362-374.
    13. Melnikov, Alexander & Romaniuk, Yulia, 2006. "Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 310-329, December.
    14. Lin, Bing-Huei, 1999. "Fitting the term structure of interest rates for Taiwanese government bonds," Journal of Multinational Financial Management, Elsevier, vol. 9(3-4), pages 331-352, November.
    15. Tse, Y.K., 1997. "Short-term interest rate models and generation of interest rate scenarios," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(3), pages 475-480.
    16. Tian, Junfang & Zhang, H.M. & Treiber, Martin & Jiang, Rui & Gao, Zi-You & Jia, Bin, 2019. "On the role of speed adaptation and spacing indifference in traffic instability: Evidence from car-following experiments and its stochastic model," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 334-350.
    17. Gollier, Christian, 2002. "Time Horizon and the Discount Rate," Journal of Economic Theory, Elsevier, vol. 107(2), pages 463-473, December.
    18. Robert R. Bliss & Ehud I. Ronn, 1997. "Callable U.S. Treasury bonds: optimal calls, anomalies, and implied volatilities," FRB Atlanta Working Paper 97-1, Federal Reserve Bank of Atlanta.
    19. Tucker, A. L. & Wei, J. Z., 1998. "Valuation of LIBOR-Contingent FX options," Journal of International Money and Finance, Elsevier, vol. 17(2), pages 249-277, April.
    20. Hans Dewachter & Leonardo Iania & Marco Lyrio, 2014. "Information In The Yield Curve: A Macro‐Finance Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(1), pages 42-64, January.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    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:gam:jecomi:v:12:y:2024:i:3:p:73-:d:1359993. 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: MDPI Indexing Manager The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (email available below). General contact details of provider: https://www.mdpi.com .

    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.