On the Calibration of the Kennedy Model

Dalma Tóth-Lakits () and Miklós Arató
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Dalma Tóth-Lakits: Department of Probability Theory and Statistics, Eötvös Loránd University, 1117 Budapest, Hungary
Miklós Arató: Department of Probability Theory and Statistics, Eötvös Loránd University, 1117 Budapest, Hungary

Mathematics, 2024, vol. 12, issue 19, 1-29

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.

Keywords: Kennedy model; calibration; term structure model; option pricing; interest rate swap; Gaussian random field; Heath–Jarrow–Morton framework; HJM model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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