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

Flavia Antonacci,Marco Papi,Cristina Costantini

doi:10.3390/math9101152

Flavia Antonacci, Marco Papi + Show 1 more

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https://doi.org/10.3390/math9101152

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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.

Highlights

The short-term interest rate is an essential component of all bond and derivative prices, but it is not directly observable
In a recent paper [21], we proposed a model for the joint evolution of the inflation rate, the central bank official interest rate, and the short-term interest rate: to the best of our knowledge, this is the first model that takes into account the interaction between the above two macroeconomic factors and the short rate
We considered the model that we proposed in a previous paper [21] to describe the joint evolution of inflation, the central bank interest rate, and the short-term interest rate

Summary

Introduction

The short-term interest rate is an essential component of all bond and derivative prices, but it is not directly observable. A sound and reliable method for estimating it and possibly predicting it, at least on a short time horizon, is valuable. Ever since the 1980s, many models have been proposed to describe the short-term interest rate dynamics (see the seminal work [1]). There have been attempts to consider models that incorporate macroeconomic factors. There is empirical and theoretical evidence that bond prices, inflation, interest rates, monetary policy, and output growth are related. See Akram and Li [2] for a recent discussion of the role of interest rates

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