Kalman Filtering of Generalized Vasicek Term Structure Models

Babbs, Simon H.; Nowman, K. Ben

doi:10.2307/2676248

Cited by 231 publications

(162 citation statements)

References 28 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%

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%

A Dynamic Model for the Forward Curve

et al. 2005

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“…In the context of interest rate models Gaussian examples can be found in Babbs and Nowman (1999) and Lund (1997), who estimate a two-factor generalized Vasicek model.…”

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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“…This filtering-based calibration approach allows us to use the short term rate as an unobservable variable rather than using a proxy for it and to use potentially noisy yield data from which to estimate the short rate. Similar approaches have been previously employed in Babbs and Nowman (1999), Rossi (2004), Gravelle and Morley (2005) To generate scenarios of uncertain future interest rates (and hence the yields, which are affine functions of short rate for the chosen short term rate model) evolving through time, we use a trinomial recombining lattice. Using a recombining lattice is an industry standard way of modeling asset price or interest rate evolution for pricing purposes.…”

Section: The Debt Management Problemmentioning

confidence: 99%

A mixed integer linear programming model for optimal sovereign debt issuance

Date

Canepa

Abdel-Jawad

2011

European Journal of Operational Research

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Governments borrow funds to finance the excess of cash payments or interest payments over receipts, usually by issuing fixed income debt and index-linked debt. The goal of this work is to propose a stochastic optimization-based approach to determine the composition of the portfolio issued over a series of government auctions for the fixed income debt, to minimize the cost of servicing debt while controlling risk and maintaining market liquidity. We show that this debt issuance problem can be modeled as a mixed integer linear programming problem with a receding horizon. The stochastic model for the interest rates is calibrated using a Kalman filter and the future interest rates are represented using a recombining trinomial lattice for the purpose of scenario-based optimization. The use of a latent factor interest rate model and a recombining lattice provides us with a realistic, yet very tractable scenario generator and allows us to do a multi-stage stochastic optimization involving integer variables on an ordinary desktop in a matter of seconds. This, in turn, facilitates frequent re-calibration of the interest rate model and re-optimization of the issuance throughout the budgetary year allows us to respond to the changes in the interest rate environment. We successfully demonstrate the utility of our approach by out-of-sample back-testing on the UK debt issuance data.

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Kalman Filtering of Generalized Vasicek Term Structure Models

Cited by 231 publications

References 28 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 mixed integer linear programming model for optimal sovereign debt issuance

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