Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates

Antonacci, Flavia; Costantini, Cristina; Papi, Marco

doi:10.3390/math9101152

Open AccessArticle

Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates

by

Flavia Antonacci

^1,*,†,‡,

Cristina Costantini

^2,‡ and

Marco Papi

^3,‡

¹

Department of Economic Studies, University of Chieti-Pescara, 65127 Pescara, Italy

²

Department of Economic Studies and INdAM Local Unit, University of Chieti-Pescara, 65127 Pescara, Italy

³

School of Engineering, University Campus Bio-Medico, 00128 Rome, Italy

^*

Author to whom correspondence should be addressed.

^†

Current address: Viale Pindaro 42, 65127 Pescara, Italy.

^‡

These authors contributed equally to this work.

Mathematics 2021, 9(10), 1152; https://doi.org/10.3390/math9101152

Submission received: 27 April 2021 / Revised: 13 May 2021 / Accepted: 17 May 2021 / Published: 20 May 2021

(This article belongs to the Special Issue Stochastic Optimization Methods in Economics, Finance and Insurance)

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Abstract

We consider the model of Antonacci, Costantini, D’Ippoliti, Papi (arXiv:2010.05462 [q-fin.MF], 2020), which describes the joint evolution of inflation, the central bank interest rate, and the short-term interest rate. In the case when the diffusion coefficient does not depend on the central bank interest rate, we derive a semi-closed valuation formula for contingent derivatives, in particular for Zero Coupon Bonds (ZCBs). By using ZCB yields as observations, we implement the Kalman filter and obtain a dynamical estimate of the short-term interest rate. In turn, by this estimate, at each time step, we calibrate the model parameters under the risk-neutral measure and the coefficient of the risk premium. We compare the market values of German interest rate yields for several maturities with the corresponding values predicted by our model, from 2007 to 2015. The numerical results validate both our model and our numerical procedure.

Keywords: inflation; short-term interest rate; Kalman filter; calibration

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MDPI and ACS Style

Antonacci, F.; Costantini, C.; Papi, M. Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates. Mathematics 2021, 9, 1152. https://doi.org/10.3390/math9101152

AMA Style

Antonacci F, Costantini C, Papi M. Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates. Mathematics. 2021; 9(10):1152. https://doi.org/10.3390/math9101152

Chicago/Turabian Style

Antonacci, Flavia, Cristina Costantini, and Marco Papi. 2021. "Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates" Mathematics 9, no. 10: 1152. https://doi.org/10.3390/math9101152

APA Style

Antonacci, F., Costantini, C., & Papi, M. (2021). Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates. Mathematics, 9(10), 1152. https://doi.org/10.3390/math9101152

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates

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