Short-term Interest Rate Models 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.

Bayesian testing for short term interest rate models

In empirical finance, interest rate models have been widely used for modeling short-term interest rate. Under the framework of the hypothesis testing, this paper provides a Bayesian approach for comparing a range of alternative models. These compared models are nested in a general single-factor diffusion process for the short-term interest rate, with each alternative model indexed by the level effect parameter for the volatility. The performance of the developed procedure is illustrated by an empirical example of Eurodollar deposit rates.

Плотности вероятностей процессов процентных ставок доходности

The processes of short-term interest rates rise to many changes in market indices, as well as form the basis of determining the value of market assets and commercial contracts. A special role they play in calculating the term structure of the yield. Therefore, the development of mathematical models of these processes is extremely interesting for financial analysts and market research issues. There are many versions of change of short-term risk-free interest rates in the framework of the theory of diffusion processes. However, there is still no such a model, which would be the basis for building a term structure of yields close to existing on a real financial market. It is interesting to analyze the existing models in order to clarify their features in a probabilistic sense, in more detail than has been done by their creators and users. To this end, the paper examines the marginal probability density of the diffusion processes generated by sixteen models of short-term interest rates, that allow obtain densities in an analytical form. Here will be made such analysis for the family of models used by the authors of papers that are widely known in their fit to the actual time series of yield. All considered models belong to the class of diffusion that generate processes, where a specific setting of drift and volatility defines one or another particular model. Some models, such as the Vasicek model, Cox – Ingersoll – Ross, geometric Brownian motion, Ahn – Gao, are well documented in the literature, but nevertheless their properties are listed here for convenience of comparison with other, less well-known or unstudied models. Other densities are described for the first time. The proposed analysis will be useful to the reader to determine the most appropriate models of short-term rates in the determination of the term structure of zero-coupon yield approximating actually observed, as far as possible, by the best way. Analysis scheme reduces to solution of the forward Kolmogorov equation for the stationary probability density and, if necessary, discuss its features and the first four moments are calculated, usually of interest in practice. It is shown that for the models the coefficients of skewness and kurtosis, defined by moments third and fourth order, depend on a single parameter, that called as the form parameter density, which, in turn, is determined only by the ratio of the variance to the square of the expectation (this corresponds to the square of the so-called coefficient of variation).

A general lower bound of parameter estimation for reflected Ornstein–Uhlenbeck processes

AbstractA reflected Ornstein–Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. It is an extended model of the traditional Ornstein–Uhlenbeck process being extensively used in finance as a one-factor short-term interest rate model. Under some mild conditions, this paper is devoted to the study of the analogue of the Cramer–Rao lower bound of a general class of parameter estimation of the unknown parameter in reflected Ornstein–Uhlenbeck processes.

Parameter estimation for generalized diffusion processes with reflected boundary

Reflected Ornstein-Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. It is an extended model of the traditional Ornstein-Uhlenbeck process being extensively used in finance as a one-factor short-term interest rate model. In this paper, under certain constraints, we are concerned with the problem of estimating the unknown parameter in the reflected Ornstein-Uhlenbeck processes with the general drift coefficient. The methodology of estimation is built upon the maximum likelihood approach and the method of stochastic integration. The strong consistency and asymptotic normality of estimator are derived. As a by-product of the use, we also establish Girsanovs theorem of our model in this paper.

Predicting short-term interest rates using Bayesian model averaging: Evidence from weekly and high frequency data

This paper examines the forecasting performance of Bayesian model averaging (BMA) for a set of single factor models of short-term interest rates. Using weekly and high frequency data for the one-month Eurodollar rate, BMA produces predictive likelihoods that are considerably better than those associated with the majority of the short-rate models, but marginally worse than those of the best model in each dataset. We also find that BMA forecasts based on recent predictive likelihoods are preferred to those based on the marginal likelihood of the entire dataset.

Exact Solvability of Stochastic Differential Equations Driven by Finite Activity Levy Processes

We consider linearizing transformations of the one-dimensional nonlinear stochastic differential equations driven by Wiener and compound Poisson processes, namely finite activity Levy processes. We present linearizability criteria and derive the required transformations. We use a stochastic integrating factor method to solve the linearized equations and provide closed-form solutions. We apply our method to a number ofstochastic differential equations including Cox-Ingersoll-Ross short-term interest rate model, log-mean reverting asset pricing model and geometric Ornstein- Uhlenbeck equation all with additional jump terms. We use their analytical solutions to illustrate the accuracy of the numerical approximations obtained from Euler and Maghsoodi discretization schemes. The means of the solutions are estimated through Monte Carlo method.

Bandwidth Selection in Pre-Smoothed Particle Filters

This paper introduces the Pre-Smoothed Particle Filter (PSPF) as a regularized alternative to the Sampling Importance Resampling (SIR) filter for non-linear state space models with additive Gaussian observation noise. The PSPF adaptively bridges the unbiased, but variance-prone, SIR filter and the biased, but less variance-prone Gaussian update filter. Our main contribution is the adaptive determination of the degree of smoothing in each time step. We illustrate the approach using examples from econometrics, namely a continuous time short term interest rate model and a dynamic stochastic general equilibrium model fitted to noisy data. The PSPF is shown to be highly suited for dynamic models with high signal-to-noise ratio, for which the SIR filter has problems.

A jump-diffusion model for the euro overnight rate

In this work we introduce a jump-diffusion process for the euro overnight rate (the European over night index average) that is able to capture the main characteristics of this rate: (i) dynamics constrained to remain in the corridor of official rates fixed by the European Central Bank; (ii) mean reversion towards the official rate on main refinancing operations; and (iii) highly discontinuous pattern (with jumps), also without variations in the official rate. After calibrating the model parameters on historical data, we implement the model to price an overnight indexed swap. Finally, a comparison between our model and the most common short-term interest rate models is presented.

Predicting Short-Term Interest Rates: Does Bayesian Model Averaging Provide Forecast Improvement?

This paper examines the forecasting qualities of Bayesian Model Averaging (BMA) over a set of single factor models of short-term interest rates. Using weekly and high frequency data for the one-month Eurodollar rate, BMA produces predictive likelihoods that are considerably better than the majority of the short-rate models, but marginally worse off than the best model in each dataset. We observe preference for models incorporating volatility clustering for weekly data and simpler short rate models for high frequency data. This is contrary to the popular belief that a diffusion process with volatility clustering best characterizes the short rate.

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

Testing the stabilization hypothesis in the UK short-term interest rates: Evidence from a GARCH-X model

The objective of this paper is to examine the validity of one of the recurring arguments made against futures markets that they give rise to price instability. The paper concentrates on the impact of futures trading on the spot market volatility of short-term interest rates. The analytical framework employed is based on a new statistical approach aiming to reconcile the traditional models of short-term interest rates and the conditional volatility processes. More specifically, this class of models aims to capture the dynamics of short-term interest rate volatility by allowing volatility to depend on both scale effects and information shocks. Using a GARCH-X and asymmetric GARCH-X model four main conclusions emerge from the present study. First, the empirical results suggest that there is an indisputable change in the nature of volatility with evidence of mean reversion after the onset of futures trading. Second, the information flow into the market has improved as a result of futures trading. Third, a stabilization effect has been detected running from the futures market to the cash market by lowering volatility levels and decreasing the risk in the spot market. Finally, trying to capture the leverage effect the findings suggest that positive shocks have a greater impact on volatility than negative shocks.

Bayesian, MLE, and GMM Estimation of a Spot Rate Model

ABSTRACT We develop Markov chain Monte Carlo algorithms for estimating the parameters of the short-term interest rate model. Using Monte Carlo experiments we compare the Bayes estimators with the maximum likelihood and generalized method of moments estimators. We estimate the model using the Japanese overnight call rate data.

Quasi-maximum likelihood estimates of Kiwi short-term interest rate

This paper examines various short-term interest rate models in New Zealand. We estimate ten stochastic models of short-term interest rates using Quasi-maximum Likelihood Estimation. All models examined allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find no evidence of mean reversion but strong evidence of the need for the volatility of interest rate changes to be highly sensitive to the level of the Kiwi short rate. Specifically, we find the conditional volatility of the Kiwi short rate is monotonically increasing with a convex shape. We also find that the dependence of the conditional volatility of the Kiwi short rate on the level of the interest rate is significantly higher than is generally assumed by the traditional models. Finally, we find that the AS model outperforms all remaining nine models, the CKLS beats seven models, except for the CEV model, whereas the CEV beats the GBM, Dothan, and the CIR VR.

Short‐term interest rate models: valuing interest rate derivatives using a Monte‐Carlo approach

AbstractThis paper provides an accessible description and several examples of how to use Monte‐Carlo simulation to value interest rate derivatives when the short rate follows an arbitrary time series process. We compare the values of various interest rate derivatives using closed‐form solutions (when available), the Hull and White (1994) trinomial tree procedure, and a Monte‐Carlo simulation technique. We show that the simulation technique can be applied to more complex short rate processes by examining short rate models where the dynamics are too complicated for any tree or lattice approach and closed‐form valuation formulae are unavailable. In a practical empirical setting, we weigh the advantages and disadvantages of the simulation approach against competing approaches.

On the robustness of short–term interest rate models

This paper investigates the robustness of a range of short–term interest rate models. We examine the robustness of these models over different data sets, time periods, sampling frequencies, and estimation techniques. We examine a range of popular one–factor models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find that parameter estimates are highly sensitive to all of these factors in the eight countries that we examine. Since parameter estimates are not robust, these models should be used with caution in practice.

On the Specification of the Drift and Diffusion Functions for Continuous‐time Models of the Spot Interest Rate*

This paper explores the specification of drift and diffusion functions for continuous-time short-term interest rate models. Various forms for the drift and diffusion of 7-day Eurodollar rates are proposed and then estimated by discrete maximum-likelihood. The results suggest that a nonparametric specification of drift and volatility in terms of orthogonal polynomial expansions is effective in eliminating problems of parameter identification encountered previously. Some evidence is found to support the claim that the drift of the short term interest rate is nonlinear.

The volatility of Japanese interest rates: evidence for Certificate of Deposit and Gensaki rates

In this paper, we apply the recently introduced Gaussian estimation methodology in the estimation of a range of one factor short-term interest rate models on Japanese Certificate of Deposit (CD) and Gensaki interest rates. For Japan, the relationship between the volatility of rates and the level of rates is smaller than that reported by Chan, Karolyi, Longstaff, and Sanders (CKLS) [J. Finance 47 (1992) 1209.] for the US. We find, generally, that the CEV model performs well for these rates in terms of data fit.

An international comparison of pricing callable and puttable bonds in international financial markets

Outlines recent research on short term interest rate models and applies Baron‐Adesi et al’s (1999) Box method to value default free bonds and contingent claims. Uses Episcopo’s (1999) historical interbank estimates of the Chan, Karolyi, Longstaff and Sanders (1992) model for Australia, Belgium, Germany, Japan, the Netherlands, New Zealand and Switzerland to calculate implied bond and contingent claim prices; and briefly discusses the results for each country. Finds both default free bonds and callable/puttable bond prices are sensitive to the interest rate model used.

A short term interest rate model

This paper suggests a short term interest rate model. It incorporates inflation rate, market variance, market net growth rate and market volatility trend. Empirical evidence from different markets supports the model.