Estimating the Short Rate from the Term Structures in the Vasicek Model

Halgašová, Jana; Stehlíková, Beáta; Bučková, Zuzana

doi:10.2478/tmmp-2014-0029

Cited by 3 publications

(6 citation statements)

References 4 publications

(6 reference statements)

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“…, n. Our aim is to estimate the domestic short rate r di for each observation time, together with the model parameters. We follow the approach of [13], [14] (where the following objective function was used to estimate the parameters, while the short rate was approximated by a proxy), [8], [2] (where it was used to estimate the short rate as well) and define the objective function…”

Section: Algorithm For Estimating the Short Rate In A Model With Zero Correlationmentioning

confidence: 99%

“…Estimation of the European parameters and the short rate corresponds to the estimation of the one-factor Vasicek model. This problem has been studied in [8] and the procedure from the paper yields accurate results using a simple optimization procedure -the main optimization is only one-dimensional and in order to evaluate the function at a certain point, we need to estimate one linear regression model (i.e., run a quadratic optimization problem). The first step of our algorithm is therefore an application of the algorithm from [8].…”

Section: Algorithm For Estimating the Short Rate In A Model With Zero Correlationmentioning

confidence: 99%

“…This problem has been studied in [8] and the procedure from the paper yields accurate results using a simple optimization procedure -the main optimization is only one-dimensional and in order to evaluate the function at a certain point, we need to estimate one linear regression model (i.e., run a quadratic optimization problem). The first step of our algorithm is therefore an application of the algorithm from [8]. Resulting estimates of the parameters b 1 , b 2 , σ e and the values of the short rate r ei for i = 1, 2, .…”

Section: Algorithm For Estimating the Short Rate In A Model With Zero Correlationmentioning

confidence: 99%

“…Also, its behaviour provides interesting information about the economy. We consider the approach of [8] (for the Vasicek model) and [2] (for the short rate as a sum of two unobservable processes), which uses a least squares methodology applied to the data of interest rates with different maturities. Furthermore, since Vasicek model is a building block of the convergence model which we consider, the algorithm [8] will serve as a first step of our estimation procedure.…”

Section: Introductionmentioning

confidence: 99%

“…Estimates from a sample calibration: European parameters a 1 , a 2 , σ 2 e (using algorithm from[8]) and domestic parameters b 1 , b 2 , σ 2…”

mentioning

confidence: 99%

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Estimating the Domestic Short Rate in a Convergence Model of Interest Rates

Bučková

Girová

Stehlíková

2020

Tatra Mountains Mathematical Publications

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In this paper we study the convergence model of interest rates by Corzo and Schwartz. It models the situation when a country is going to enter a monetary union, for example the eurozone. We are interested in estimating the underlying short rate, which is a theoretical variable, not observed on the market. We use the procedure already employed for the Vasicek model to the eurozone data and for the case of a zero correlation we show that a similar procedure can be used also for the estimation of the domestic parameters and the short rate values. The assumption of the zero correlation allows us to simplify the optimization problem, but using simulations we show that our algorithm is robust to the specification of the correlation. It estimates the short rate with a high precision also in the original case of a nonzero correlation, as well as in the case of a dynamic correlation, when the correlation is modelled as a function of time. Finally, we use the algorithm to real market data and estimate the short rate before adoption of the euro currency in Slovakia, Estonia, Latvia and Lithuania.

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Section: Algorithm For Estimating the Short Rate In A Model With Zero Correlationmentioning

confidence: 99%

Section: Algorithm For Estimating the Short Rate In A Model With Zero Correlationmentioning

confidence: 99%

Section: Algorithm For Estimating the Short Rate In A Model With Zero Correlationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Estimates from a sample calibration: European parameters a 1 , a 2 , σ 2 e (using algorithm from[8]) and domestic parameters b 1 , b 2 , σ 2…”

mentioning

confidence: 99%

See 3 more Smart Citations

Estimating the Domestic Short Rate in a Convergence Model of Interest Rates

Bučková

Girová

Stehlíková

2020

Tatra Mountains Mathematical Publications

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State-space of the Vasicek model for long-term bonds with Kalman filter

2023

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In this paper, a time-consistent and arbitrage-free state space for the one-, two-, and three-factor Vasicek models for long-term bonds is constructed. To account for the uncertainty in long-term bond yields, we propose a stochastic time-dependent mean-reversion model. The state-space model allows for the computation of measurement errors from observed yields. Appropriate state and measurement linear equations are derived to allow the use of the Kalman filter for model implementation. Based on weekly South African Government Bonds from February 2010 to February 2021, we give parameter estimates for the one-factor, two-factor, and three-factor models. The results from the study show that the developed model can fit the term structure of very long-term bonds.

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Numerical and analytical methods for bond pricing in short rate convergence models of interest rates

Buckova,

Stehlikova,

Sevcovic

2016

Preprint

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In this survey paper we discuss recent advances on short interest rate models which can be formulated in terms of a stochastic differential equation for the instantaneous interest rate (also called short rate) or a system of such equations in case the short rate is assumed to depend also on other stochastic factors. Our focus is on convergence models, which explain the evolution of interest rate in connection with the adoption of Euro currency. Here, the domestic short rate depends on a stochastic European short rate. In short rate models, the bond prices, which determine the term structure of interest rate, are obtained as solutions to partial differential equations. Analytical solutions are available only in special cases; therefore we consider the question of obtaining their approximations. We use both analytical and numerical methods to get an approximate solution to the partial differential equation for bond prices.

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Estimating the Short Rate from the Term Structures in the Vasicek Model

Cited by 3 publications

References 4 publications

Estimating the Domestic Short Rate in a Convergence Model of Interest Rates

Estimating the Domestic Short Rate in a Convergence Model of Interest Rates

State-space of the Vasicek model for long-term bonds with Kalman filter

Numerical and analytical methods for bond pricing in short rate convergence models of interest rates

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