Dynamics Of Short-term Interest Rate Research Articles

Dynamic characteristics of expectations of short-term interest rate and a generalized Vasicek model

This study's principal mathematical deduction exploits the importance of the specification of long-term equilibrium level in the mean-reversion short-term interest rate model—such as the CKLS (Chan, Karolyi, Longstaff, and Sanders) model—to describe the dynamic characteristics of future short-term interest rate expectations, especially long-horizon expectations. Therefore, we present a preferred model by introducing a stochastic long-run equilibrium level factor to extend the specifications of the Vasicek model's short-term interest rate dynamics. Using this new type of short-term interest rate as a driver we develop a two-factor affine arbitrage-free model of term structure, the generalized Vasicek mode. The empirical results show that the model not only has a good sample fitting ability to the Chinese government bond yield curve, but also has better performance in capturing the dynamic characteristics of short-term interest rates and short-term interest rate expectations. This study provides not only a promising avenue for future research on improving interest rate modeling techniques and their practical applications in the financial industry but also a new literature base for accurately identifying public expectations and explaining the underlying mechanisms of expectation changes.

Parametric Estimation of Diffusion Processes: A Review and Comparative Study

This paper provides an in-depth review about parametric estimation methods for stationary stochastic differential equations (SDEs) driven by Wiener noise with discrete time observations. The short-term interest rate dynamics are commonly described by continuous-time diffusion processes, whose parameters are subject to estimation bias, as data are highly persistent, and discretization bias, as data are discretely sampled despite the continuous-time nature of the model. To assess the role of persistence and the impact of sampling frequency on the estimation, we conducted a simulation study under different settings to compare the performance of the procedures and illustrate the finite sample behavior. To complete the survey, an application of the procedures to real data is provided.

Interest rates calibration with a CIR model

PurposeThe purpose of this paper is to model interest rates from observed financial market data through a new approach to the Cox–Ingersoll–Ross (CIR) model. This model is popular among financial institutions mainly because it is a rather simple (uni-factorial) and better model than the former Vasicek framework. However, there are a number of issues in describing interest rate dynamics within the CIR framework on which focus should be placed. Therefore, a new methodology has been proposed that allows forecasting future expected interest rates from observed financial market data by preserving the structure of the original CIR model, even with negative interest rates. The performance of the new approach, tested on monthly-recorded interest rates data, provides a good fit to current data for different term structures.Design/methodology/approachTo ensure a fitting close to current interest rates, the innovative step in the proposed procedure consists in partitioning the entire available market data sample, usually showing a mixture of probability distributions of the same type, in a suitable number of sub-sample having a normal/gamma distribution. An appropriate translation of market interest rates to positive values has been introduced to overcome the issue of negative/near-to-zero values. Then, the CIR model parameters have been calibrated to the shifted market interest rates and simulated the expected values of interest rates by a Monte Carlo discretization scheme. We have analysed the empirical performance of the proposed methodology for two different monthly-recorded EUR data samples in a money market and a long-term data set, respectively.FindingsBetter results are shown in terms of the root mean square error when a segmentation of the data sample in normally distributed sub-samples is considered. After assessing the accuracy of the proposed procedure, the implemented algorithm was applied to forecast next-month expected interest rates over a historical period of 12 months (fixed window). Through an error analysis, it was observed that our algorithm provides a better fitting of the predicted expected interest rates to market data than the exponentially weighted moving average model. A further confirmation of the efficiency of the proposed algorithm and of the quality of the calibration of the CIR parameters to the observed market interest rates is given by applying the proposed forecasting technique.Originality/valueThis paper has the objective of modelling interest rates from observed financial market data through a new approach to the CIR model. This model is popular among financial institutions mainly because it is a rather simple (uni-factorial) and better model than the former Vasicek model (Section 2). However, there are a number of issues in describing short-term interest rate dynamics within the CIR framework on which focus should be placed. A new methodology has been proposed that allows us to forecast future expected short-term interest rates from observed financial market data by preserving the structure of the original CIR model. The performance of the new approach, tested on monthly data, provides a good fit for different term structures. It is shown how the proposed methodology overcomes both the usual challenges (e.g. simulating regime switching, clustered volatility and skewed tails), as well as the new ones added by the current market environment (particularly the need to model a downward trend to negative interest rates).

Nonparametric conditional density estimation of short-term interest rate movements: procedures, results and risk management implications

This article shows how to estimate the conditional density of daily changes in the 3-month T-bill rate, using an extension of the kernel-based estimator proposed by Rosenblatt (1969 Rosenblatt, M. 1969. “Conditional probability density and regression estimators”. In Multivariate Analysis II, Edited by: Krishnaiah, PR. 25–31. New York: Academic Press. [Google Scholar]). The shape of the estimated density is allowed to vary with both the level and the lagged change in rates. Due to the nonparametric character of the estimation procedure, the model produces conditional quantile estimates that are based only on the data and are independent of the modellers’ assumptions. The obtained results do not support the assumption of systematically mean-reverting behaviour underlying some theoretical models of short-term interest rate dynamics. However, they clearly indicate the presence of nonlinear first-order autocorrelation and volatility clustering effects, as well as a positive relationship between yield volatility and level.

A BAYESIAN ANALYSIS FOR SHORT-TERM INTEREST RATE MODELS AND ITS APPLICATIONS

This paper presents an analysis of models for Japanese short-term inter- est rate. The models are constructed based on mean reverting model using Bayesian method to capture the dynamics of short-term interest rate. The parameters of our models are estimated by marginal likelihood and posterior expectation and we shall make model selection using the information criterion EIC(extended information cri- terion). An application of the models will be implemented using weekly Japanese average interest rates on certificates of deposit (new issues) less than 30 days in the period from January 2001 to December 2008. 1 Introduction Correct modeling of the short-term interest rate is essential in finace, as it is this rate that is fundamental to the pricing of securities and important for risk man- agement. In the study of the short-term interest rate dynamics, various models have been suggested. There are examples of these models, such as Vasicek model by Vasicek(1977), CIR model by Cox, Ingersoll and Ross(1985) and so on. An empirical comparison of these models was made by Chan, Karolyi, Longstaff and Sanders(1992). In the paper, the param- eters are estimated by generalized method of moments(GMM) and they implemented the hypothesis testing methods developed by Newey and West for evaluation of the models. In the parameter estimation of mean reverting model using GMM, it is known that the results are easy to be influenced by an initial values, and it becomes often unstable. Recently, Ahangarani(2005) employed maximum likelihood method for parameter esti- mation and log likelihood ratio test for model selection, and Kawada(2007) implemented GMM and made model selection using the information criterion EIC(extended information criterion) for various short-term interest rate models. Another articles of the interest rate model, using Bayesian framework, Jones(2003) published study about nonlinear drift of the interest rate model in detail, and Gray(2005) studied continuous time short rate models and the parameters estimated by Markov chain Monte Carlo(MCMC) method. Sanford and Martin(2006) made estimation using MCMC algorithm and model selection is made by Bayes factors for each model calculated using Savage-Dickey density ratio. In addition, a recent study by Hong and Lin(2006) examined a variety of short-term interest rate mod- els including the single-factor diffusion models, GARCH models, Markov regime-switching models and jump-diffusion models for Chinese rates. However, more useful models which capture the dynamics of the short-term interest rate are needed. In this paper, we suggest two hierarchical Bayes models based on mean reverting model. The parameters of the models are treated as random variables so that we have to consider appropriate prior distributions for them. By regarding parameters as random variables, we can consider that model construction and estimation involve necessarily some uncertainty and utilize the prior information of interest rate. In the first hierarchical Bayes model, we assume that volatility is constant, and in the second one, it depends on the

Nonparametric estimation of convergence of interest rates: Effects on bond pricing

We present and estimate a model of short term interest rate dynamics where we incorporate the convergent behavior of interest rates implied by the transition to EMU. We apply this model to data of two EMU countries - Spain and Italy - and compare the performance, in terms of accuracy of bond pricing, of this two-factor convergence model with alternative specifications. Nonparametric techniques are used for the estimation of the processes. The two-factor model which accounts for the convergence with Europe of the domestic economies, obtains better results, especially for short-term assets, than alternative models. The results of the nonparametric specifications are shown to be significantly better than those of parametric alternatives.

Short-term interest rate dynamics: a spatial approach

We use new fully functional methods to describe and study the dynamics of the short-term interest rate process in continuous-time. The suggested procedure exploits the spatial properties, embodied in the local time process, of the diffusion of interest, and is robust against deviations from stationarity. Our results indicate that the misspecification of a standard constant elasticity of variance model with linear mean-reverting drift cannot be attributed to the nonlinear behavior of the infinitesimal first moment of the short-term interest rate process at high rates. Rather, it should be attributed to the martingale nature of the process over most of its empirical range (i.e., between 3% and about 15%).

Nonparametric Estimation of Convergence of Interest Rates: Effects on Bond Pricing

We present and estimate, using nonparametric regression techniques, a model of short term interest rate dynamics and use the estimation to value bonds. We study the case of two European countries - Spain and Italy - that belong to EMU, and compare the resulting bond prices of a one factor model with that of a two factor, the second factor being a stochastic mean. The pricing errors for both models are 34% smaller than those reported on the parametric literature. Furthermore, the two factor model, which takes into account the convergence with Europe of the domestic economies, obtains better results than the one factor model. Our findings give strong support to the importance of a correct specification of the volatility of interest rates.

Do We Need Multi-Country Models to Explain Exchange Rate and Interest Rate Dynamics?

This paper examines characterizations of exchange rate and short-term interest rate dynamics, based on the implications of multi-country versions of the Cox, Ingersoll, and Ross (1985) class of term structure models. The countries considered are the US, Germany, Japan, and the UK. Our tests reveal that multi-country models are, in some cases, better able to explain the dynamics of exchange rates and interest rates than two-country and single-country models respectively. This is particularly true for the Japanese interest rate as well as the rate of appreciation of the Deutsche mark relative to the US dollar. Our inference is conducted using the small-sample distributions of test statistics, in addition to their asymptotic distributions.