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

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
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