A State‐space Approach to Estimate and Test Multifactor Cox‐ingersoll‐ross Models of the Term Structure

Geyer, Alois; Pichler, Stefan

doi:10.1111/j.1475-6803.1999.tb00717.x

Cited by 108 publications

(84 citation statements)

References 24 publications

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“…We can then run the Kalman filter to estimate the state variables by iterating between the prediction equations and the updating equations as in DeJong and Santa-Clara (1999), Geyer and Pichler (1999) and Babbs and Nowman (1999). 13 We provide a copy of the standard equations of the Kalman filter in Appendix A.4.…”

Section: By Viewing M(t) and D(t)mentioning

confidence: 99%

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A Dynamic Model for the Forward Curve

et al. 2005

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This article develops and estimates a dynamic arbitrage-free model of the current forward curve as the sum of (i) an unconditional component, (ii) a maturity-specific component and (iii) a date-specific component. The model combines features of the Preferred Habitat model, the Expectations Hypothesis (ET) and affine yield curve models; it permits a class of low-parameter, multiple state variable dynamic models for the forward curve. We show how to construct alternative parametric examples of the three components from a sum of exponential functions, verify that the resulting forward curves satisfy the Heath-Jarrow-Morton (HJM) conditions, and derive the risk-neutral dynamics for the purpose of pricing interest rate derivatives. We select a model from alternative affine examples that are fitted to the Fama-Bliss Treasury data over an initial training period and use it to generate out-of-sample forecasts for forward rates and yields. For forecast horizons of 6 months or longer, the forecasts of this model significantly outperform those from common benchmark models. (JEL C53, E43, E47)The structure of forward rates for fixed maturity loans to begin at various dates in the future can be inferred from the prices of Treasury securities or directly observed from the extremely active Eurodollar Futures market. The constellation of these rates (or of the related yields) plays a central role in the allocation of capital. The random behavior of this ''yield curve''-or the relationship between the yields and the term to maturity-is a subject of considerable theoretical and empirical study.We would like to thank the editor, Yacine Aït-Sahalia, and two anonymous referees for their guidance. We are also grateful to Amir Yaron, Michael Brandt, Francis Diebold and seminar participants at The University of Pennsylvania, Singapore Management University, the 2005 Financial Management

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Section: By Viewing M(t) and D(t)mentioning

confidence: 99%

“…In the empirical implementation, a simple and common way of enforcing this restriction is to replace the values of the state variables that do breach the constraints with ones that just satisfy it. See Chen and Scott (2002) and Geyer and Pichler (1999) for further examples of such restrictions in a Kalman filter.…”

Section: By Viewing M(t) and D(t)mentioning

confidence: 99%

A Dynamic Model for the Forward Curve

et al. 2005

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“…This approximation is needed because of the non-Gaussian nature of the problem, which can be compared to linearizing a non-linear function in the typical Kalman filtering applications. Duan and Simonato (1999) and Geyer and Pichler (1998) apply Kalman filter to estimate and test exponential-affine term structure models for both the Gaussian and non-Gaussian cases.…”

Section: Empirical Estimation Of the Joint Stochastic Processmentioning

confidence: 99%

“…Following Duan and Simonato (1999) and Geyer and Pichler (1998) we modify the standard Kalman filter by simply replacing any negative element of the convenience yield estimate with zero.…”

Section: Empirical Estimation Of the Joint Stochastic Processmentioning

confidence: 99%

A Two-Factor Model for Commodity Prices and Futures Valuation

Ribeiro¹,

Hodges

2004

SSRN Journal

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This paper develops a reduced form two-factor model for commodity spot prices and futures valuation. This model extends the Gibson and Schwartz (1990)-Schwartz (1997) two-factor model by adding two new features. First the Ornstein-Uhlenbeck process for the convenience yield is replaced by a Cox-Ingersoll-Ross (CIR) process. This ensures that our model is arbitrage-free. Second, spot price volatility is proportional to the square root of the convenience yield level. We empirically test both models using weekly

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“…important term structure models, from Vasicek (1977) and CIR one-factor models to three-factor models like the one presented in Gong and Remolona (1997a). An additional feature of these models is that they allow the estimation of the term structure simultaneously on a cross-section and a time-series basis.…”

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A two-factor model of the German term structure of interest rates

Cassola

Luís

2003

Applied Financial Economics

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. www.econstor.eu Modelling, Frankfurt am Main, 30 March 1999, the European Economics and Financial Centre Conference, Maribor, 30 June 1999, the University of York, 4 November 1999, Universidade Católica Portuguesa, Lisbon, 14 February 2000 In this paper we show that a two-factor constant volatility model provides an adequate description of the dynamics and shape of the German term structure of interest rates from 1972 up to 1998. The model also provides reasonable estimates of the volatility and term premium curves. Following the conjecture that the two factors driving the German term structure of interest rates represent the H[-DQWH real interest rate and the expected inflation rate, the identification of one factor with expected inflation is discussed. Our estimates are obtained using a Kalman filter and a maximum likelihood procedure including in the measurement equation both the yields and their volatilities. Terms of use: Documents in EconStor may E U R O P E A N C E N T R A L B A N K W O R K I N G PA P E R S E R I E S WORKING PAPER NO. 46 A TWO-FACTOR MODEL OF THE GERMAN TERM STRUCTURE OF INTEREST RATES BY NUNO CASSOLA AND JORGE BARROS LUÍS March 2001 E U R O P E A N C E N T R A L B A N K W O R K I N G PA P E R S E R I E S * Previous versions of this paper were presented at the ESCB Workshop on Yield Curve-(/ &ODVVLILFDWLRQ FRGHV E43, G12..H\ ZRUGV expectations hypothesis; term premiums; pricing kernels; affine model One-factor models were the first step in modelling the term structure of interest rates. These models are grounded on the estimation of bond yields as functions of the short-term interest rate. Vasicek (1977) and Cox HW DO. (1985) (CIR hereafter) are the seminal papers within this literature. However, one factor models do not overcome the discrepancy between the theoretical mean yield curve implied by the time-series properties of bond yields and the observed curves that are substantially more concave than implied by the theory (see, for instance, Backus HW DO (1998)).One answer to this question has been provided by multifactor affine models, that consider bond yields as functions of several macroeconomic and financial variables, observable or latent. Affine models are easier to estimate than binomial models, 1 given that the parameters are linear in both the maturity of the assets and the number of factors. 2Most papers have focused on the U.S. term structure. The pronounced humpshape of the US yield curve and the empirical work pio...

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A State‐space Approach to Estimate and Test Multifactor Cox‐ingersoll‐ross Models of the Term Structure

Cited by 108 publications

References 24 publications

A Dynamic Model for the Forward Curve

A Dynamic Model for the Forward Curve

A Two-Factor Model for Commodity Prices and Futures Valuation

A two-factor model of the German term structure of interest rates

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