Calibration of the Ueno’s Shadow Rate Model of Interest Rates

Lenka Košútová and Beáta Stehlíková ()
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Lenka Košútová: Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia
Beáta Stehlíková: Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia

Mathematics, 2024, vol. 12, issue 22, 1-12

Abstract: Shadow rate models of interest rates are based on the assumption that the interest rates are determined by an unobservable shadow rate. This idea dates back to Fischer Black, who understood the interest rate as an option that cannot become negative. Its possible zero values are consequences of negative values of the shadow rate. In recent years, however, the negative interest rates have become a reality. To capture this behavior, shadow rate models need to be adjusted. In this paper, we study Ueno’s model, which uses the Vasicek process for the shadow rate and adjusts its negative values when constructing the short rate. We derive the probability properties of the short rate in this model and apply the maximum likelihood estimation method to obtain the parameters from the real data. The other interest rates are—after a specification of the market price of risk—solutions to a parabolic partial differential equation. We solve the equation numerically and use the long-term rates to fit the market price of risk.

Keywords: shadow rate model; maximum likelihood estimation; partial differential equation; market price of risk; calibration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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