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On the Calibration of the Kennedy Model

Author

Listed:
  • Dalma Tóth-Lakits

    (Department of Probability Theory and Statistics, Eötvös Loránd University, 1117 Budapest, Hungary
    These authors contributed equally to this work.)

  • Miklós Arató

    (Department of Probability Theory and Statistics, Eötvös Loránd University, 1117 Budapest, Hungary
    These authors contributed equally to this work.)

Abstract

The Kennedy model offers a robust framework for modeling forward rates, leveraging Gaussian random fields to accommodate emerging phenomena such as negative rates. In our study, we employ maximum likelihood estimations to determine the parameters of the Kennedy field, utilizing Radon–Nikodym derivatives for enhanced accuracy. We introduce an efficient simulation method for the Kennedy field and develop a Black–Scholes-like analytical pricing formula for diverse financial assets. Additionally, we present a novel parameter estimation algorithm grounded in numerical extreme value optimization, enabling the recalibration of parameters based on observed financial product prices. To validate the efficacy of our approach, we assess its performance using real-world par swap rates in the latter part of this article.

Suggested Citation

  • Dalma Tóth-Lakits & Miklós Arató, 2024. "On the Calibration of the Kennedy Model," Mathematics, MDPI, vol. 12(19), pages 1-29, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3059-:d:1489094
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    References listed on IDEAS

    as
    1. Beyna, Ingo & Wystup, Uwe, 2010. "On the calibration of the Cheyette interest rate model," CPQF Working Paper Series 25, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    2. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
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