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Short Rate (short + rate)

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  • short rate models
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    Selected Abstracts

    Specification Analysis of Diffusion Models for the Italian Short Rate

    ECONOMIC NOTES, Issue 1 2005
    Monica Gentile
    In recent years, diffusion models for interest rates became very popular. In this paper, we perform a selection of a suitable diffusion model for the Italian short rate. Our data set is given by the yields on 3-month BOT (Buoni Ordinari del Tesoro), from 1981 to 2001, for a total of 470 observations. We investigate among stochastic volatility models, paying more attention to affine models. Estimating diffusion models via maximum likelihood, which would lead to efficiency, is usually unfeasible because the transition density is not available. Recently, Gallant and Tauchen (1996) proposed a method of moments which gains full efficiency, hence its name of Efficient Method of Moments (EMM); it selects the moments as the scores of an auxiliary model, to be computed via simulation; thus, EMM is suitable to diffusions whose transition density is unknown, but which are convenient to simulate. The auxiliary model is selected among a family of densities which spans the density space. As a by-product, EMM provides diagnostics that are easy to compute and interpret. We find evidence that one-factor models and multi-factor affine models are rejected, while a logarithmic specification of the volatility provides the best fit to the data. [source]

    The Hull and White Model of the Short Rate: An Alternative Analytical Representation

    THE JOURNAL OF FINANCIAL RESEARCH, Issue 4 2002
    Dwight Grant
    Abstract Hull and White extend Ho and Lee's no-arbitrage model of the short interest rate to include mean reversion. This addition eliminates the problem of negative interest rates and has found wide application. To implement their model, Hull and White employ a sequential search process to identify the mean interest rate in a trinomial lattice at each date. In this article we extend Hull and White's work by developing an analytical solution for the mean interest rate at each date. This solution applies equally well to trinomial lattices, interest rate trees, and Monte Carlo simulation. We illustrate the analytical result by applying it to an example originally used by Hull and White and then for valuing an option on a bond. [source]

    Threshold Dynamics of Short-term Interest Rates: Empirical Evidence and Implications for the Term Structure

    ECONOMIC NOTES, Issue 1 2008
    Theofanis Archontakis
    This paper studies a nonlinear one-factor term structure model in discrete time. The short-term interest rate follows a self-exciting threshold autoregressive (SETAR) process that allows for shifts in the intercept and the variance. In comparison with a linear model, we find empirical evidence in favour of the threshold model for Germany and the US. Based on the estimated short-rate dynamics we derive the implied arbitrage-free term structure of interest rates. Since analytical solutions are not feasible, bond prices are computed by means of Monte Carlo integration. The resulting term structure captures stylized facts of the data. In particular, it implies a nonlinear relation between long rates and the short rate. [source]

    Specification Analysis of Diffusion Models for the Italian Short Rate

    ECONOMIC NOTES, Issue 1 2005
    Monica Gentile
    In recent years, diffusion models for interest rates became very popular. In this paper, we perform a selection of a suitable diffusion model for the Italian short rate. Our data set is given by the yields on 3-month BOT (Buoni Ordinari del Tesoro), from 1981 to 2001, for a total of 470 observations. We investigate among stochastic volatility models, paying more attention to affine models. Estimating diffusion models via maximum likelihood, which would lead to efficiency, is usually unfeasible because the transition density is not available. Recently, Gallant and Tauchen (1996) proposed a method of moments which gains full efficiency, hence its name of Efficient Method of Moments (EMM); it selects the moments as the scores of an auxiliary model, to be computed via simulation; thus, EMM is suitable to diffusions whose transition density is unknown, but which are convenient to simulate. The auxiliary model is selected among a family of densities which spans the density space. As a by-product, EMM provides diagnostics that are easy to compute and interpret. We find evidence that one-factor models and multi-factor affine models are rejected, while a logarithmic specification of the volatility provides the best fit to the data. [source]

    Non-linear interest rate dynamics and forecasting: evidence for US and Australian interest rates

    INTERNATIONAL JOURNAL OF FINANCE & ECONOMICS, Issue 2 2009
    David G. McMillan
    Abstract Recent empirical finance research has suggested the potential for interest rate series to exhibit non-linear adjustment to equilibrium. This paper examines a variety of models designed to capture these effects and compares both their in-sample and out-of-sample performance with a linear alternative. Using short- and long-term interest rates we report evidence that a logistic smooth-transition error-correction model is able to best characterize the data and provide superior out-of-sample forecasts, especially for the short rate, over both linear and non-linear alternatives. This model suggests that market dynamics differ depending on whether the deviations from long-run equilibrium are above or below the threshold value. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Short Rate Dynamics and Regime Shifts,

    INTERNATIONAL REVIEW OF FINANCE, Issue 3 2009
    HAITAO LI
    ABSTRACT We characterize the dynamics of the US short-term interest rate using a Markov regime-switching model. Using a test developed by Garcia, we show that there are two regimes in the data: In one regime, the short rate behaves like a random walk with low volatility; in another regime, it exhibits strong mean reversion and high volatility. In our model, the sensitivity of interest rate volatility to the level of interest rate is much lower than what is commonly found in the literature. We also show that the findings of nonlinear drift in Aït-Sahalia and Stanton, using nonparametric methods, are consistent with our regime-switching model. [source]

    PRICING IN AN INCOMPLETE MARKET WITH AN AFFINE TERM STRUCTURE

    MATHEMATICAL FINANCE, Issue 3 2004
    Virginia R. Young
    We apply the principle of equivalent utility to calculate the indifference price of the writer of a contingent claim in an incomplete market. To recognize the long-term nature of many such claims, we allow the short rate to be random in such a way that the term structure is affine. We also consider a general diffusion process for the risky stock (index) in our market. In a complete market setting, the resulting indifference price is the same as the one obtained by no-arbitrage arguments. We also show how to compute indifference prices for two types of contingent claims in an incomplete market, in the case for which the utility function is exponential. The first is a catastrophe risk bond that pays a fixed amount at a given time if a catastrophe does not occur before that time. The second is equity-indexed term life insurance which pays a death benefit that is a function of the short rate and stock price at the random time of the death of the insured. Because we assume that the occurrence of the catastrophe or the death of the insured is independent of the financial market, the markets for the catastrophe risk bond and the equity-indexed life insurance are incomplete. [source]

    On the Existence of Finite-Dimensional Realizations for Nonlinear Forward Rate Models

    MATHEMATICAL FINANCE, Issue 2 2001
    Tomas Björk
    We consider interest rate models of the Heath,Jarrow,Morton type, where the forward rates are driven by a multidimensional Wiener process, and where the volatility is allowed to be an arbitrary smooth functional of the present forward rate curve. Using ideas from differential geometry as well as from systems and control theory, we investigate when the forward rate process can be realized by a finite-dimensional Markovian state space model, and we give general necessary and sufficient conditions, in terms of the volatility structure, for the existence of a finite-dimensional realization. A number of concrete applications are given, and all previously known realization results (as far as existence is concerned) for Wiener driven models are included and extended. As a special case we give a general and easily applicable necessary and sufficient condition for when the induced short rate is a Markov process. In particular we give a short proof of a result by Jeffrey showing that the only forward rate models with short rate dependent volatility structures which generically possess a short rate realization are the affine ones. These models are thus the only generic short rate models from a forward rate point of view. [source]

    Nonlinear asymmetric models of the short-term interest rate

    THE JOURNAL OF FUTURES MARKETS, Issue 9 2006
    K. Ozgur DemirtasArticle first published online: 18 JUL 200
    This study introduces a generalized discrete time framework to evaluate the empirical performance of a wide variety of well-known models in capturing the dynamic behavior of short-term interest rates. A new class of models that displays nonlinearity and asymmetry in the drift, and incorporates the level effect and stochastic volatility in the diffusion function is introduced in discrete time and tested against the popular diffusion, GARCH, and level-GARCH models. Based on the statistical test results, the existing models are strongly rejected in favor of the newly proposed models because of the nonlinear asymmetric drift of the short rate, and the presence of nonlinearity, GARCH, and level effects in its volatility. The empirical results indicate that the nonlinear asymmetric models are better than the existing models in forecasting the future level and volatility of interest rate changes. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:869,894, 2006 [source]

    CONSISTENT MARKET EXTENSIONS UNDER THE BENCHMARK APPROACH

    MATHEMATICAL FINANCE, Issue 1 2009
    Damir Filipovi
    The existence of the growth optimal portfolio (GOP), also known as the Kelly portfolio, is vital for a financial market to be meaningful. The GOP, if it exists, is uniquely determined by the market parameters of the primary security accounts. However, markets may develop and new security accounts become tradable. What happens to the GOP if the original market is extended? In this paper we provide a complete characterization of market extensions which are consistent with the existence of a GOP. We show that a three fund separation theorem applies for the extended GOP. This includes, in particular, the introduction of a locally risk free security, the savings account. We give necessary and sufficient conditions for a consistent exogenous specification of the prevailing short rates. [source]

    Stochastic Volatility Corrections for Interest Rate Derivatives

    MATHEMATICAL FINANCE, Issue 2 2004
    Peter Cotton
    We study simple models of short rates such as the Vasicek or CIR models, and compute corrections that come from the presence of fast mean-reverting stochastic volatility. We show how these small corrections can affect the shape of the term structure of interest rates giving a simple and efficient calibration tool. This is used to price other derivatives such as bond options. The analysis extends the asymptotic method developed for equity derivatives in Fouque, Papanicolaou, and Sircar (2000b). The assumptions and effectiveness of the theory are tested on yield curve data. [source]

    A Term Structure Decomposition of the Australian Yield Curve,

    THE ECONOMIC RECORD, Issue 271 2009
    RICHARD FINLAY
    We use data on coupon-bearing Australian Government bonds and Overnight Indexed Swap (OIS) rates to estimate risk-free zero-coupon yield and forward curves for Australia from 1992 to 2007. These curves and analysts' forecasts of future interest rates are then used to fit an affine term structure model to Australian interest rates, with the aim of decomposing forward rates into expected future overnight cash rates plus term premia. The expected future short rates derived from the model are on average unbiased, fluctuating around the average of actual observed short rates. Since the adoption of inflation targeting and the entrenchment of low and stable inflation expectations, term premia appear to have declined in levels and displayed smaller fluctuations in response to economic shocks. This suggests that the market has become less uncertain about the path of future interest rates. Towards the end of the sample period, term premia have been negative, suggesting that investors may have been willing to pay a premium for Commonwealth Government securities. [source]

    Markov-Switching Mean Reversion in Short-Term Interest Rates: Evidence from East Asian Economies,

    THE ECONOMIC RECORD, Issue 263 2007
    CHEW LIAN CHUA
    This paper employs a Markov-switching approach to model the dynamics of East Asian short rates. Regime changes are incorporated in standard unit root test to reveal periodic changes in the stationarity property of interest rates. There is evidence that three of the five short rates follow a random walk process in tranquil and low rates episodes but mean-revert in periods when rates are high and volatile. Singapore short rates are characterised by a random walk process, whereas the Philippines rates behave as a mean-reverting process in both regimes. Factors such as exchange rates, monetary policy and interest rate differentials vis-à-vis US interest rates influence the likelihood of short rates being in a volatile state. The regime switching dynamics of interest rates carry important implications for policy-makers. [source]

    An Examination of Affine Term Structure Models,

    ASIA-PACIFIC JOURNAL OF FINANCIAL STUDIES, Issue 4 2009
    Suk-Joon Byun
    Abstract This paper examines the relative performance of models in the affine term structure family which includes both complete and essential affine models using Korean government bond yield data. Principal component analysis with Korean government bond yield data shows that the first three components of yields explain 97% of the total yield curve variation, and the components can be characterized as "level", "slope", and "curvature." We also estimate all three-factor affine models using a Kalman filter/quasi maximum likelihood (QML) approach. An exhaustive comparison shows that the three-factor essential affine model, A1 (3) E, in which only one factor affects the instantaneous volatility of short rates but all three factors affect the price of risk, appears to be the best model in Korea. This finding is consistent with results in Dai and Singleton (2002) and Duffee (2002) on US data and in Tang and Xia (2007) on Canadian, German, Japanese, UK and US data. [source]