Kalman filtering of consistent forward rate curves: a tool to estimate and model dynamically the term structure

Rossi, Giuliano

doi:10.1016/j.jempfin.2003.02.002

Cited by 21 publications

(18 citation statements)

References 23 publications

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“…Moreover, we see that affine processes essentially do not differ from consistent parametric models of the term structure in the sense of Filipovic (1999) and Bjork and Christensen (1999) (see De-Rossi (2004) for an application). With fixed parameters, affine processes simply offer parametric functions A and B of the maturities, which relate the evolution of the term structure to the evolution of the state space Y in a consistent way where discounted bond prices are Q-martingales.…”

Section: Model Estimation: Maximum Likelihoodmentioning

confidence: 83%

A Note on the Relation Between Principal Components and Dynamic Factors in Affine Term Structure Models

Ibsen

Almeida²

2005

Brazilian Review of Econometrics

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In econometric applications of the term structure, affine models are among the most used ones. Nevertheless, even presenting a closed form characteristic function, its estimation procedure still presents many points to be understood and difficulties to be removed. In this note, we address one of these points. Suppose we estimate an affine dynamic term structure model, and also apply principal component analysis to the interest rate database available. A very plausible question would inquire about the relation (if any) between the principal components obtained assuming no dynamic restrictions, and the dynamic factors estimated using the proposed term structure model. We answer this question when estimating a standard affine model using zero coupon data. We show that each principal component can be approximated by a linear transformation of the dynamic factors. Although simple, this is an important step to the understanding of the mechanics of dynamic affine term structure models. A numerical example using U.S. zero data illustrates the result.

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Section: Model Estimation: Maximum Likelihoodmentioning

confidence: 83%

A Note on the Relation Between Principal Components and Dynamic Factors in Affine Term Structure Models

Ibsen

Almeida²

2005

Brazilian Review of Econometrics

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“…However, in (13), it is very difficult to find the gradient of the likelihood function with respect to the parameters. This system is too involved.…”

Section: Methodology Of Estimationmentioning

confidence: 99%

“…(B H (t), t ≥ 0) is a fractional Brownian motion on some probability space (Ω, F, P ) with Hurst parameter, H. This model is used to replace the constant volatility in risky asset model. Some used this model as a short rate model [De Rossi, 2004]. Consider the measurement dynamics as…”

Section: Model Simplificationmentioning

confidence: 99%

Maximum Likelihood Estimation With Dynamic Measurement Errors and Application to Interest Rate Modeling

Misiran¹

2016

Int. J. of Pure and Appl. Math.

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Stochastic volatility (SV) model is widely applied in the extension of the constant volatility in Black-Scholes option pricing. In this paper, we extend the SV model driven by fractional Brownian motion (FBM). A crucial problem in its application is how the unknown parameters in the model are to be estimated. We propose the innovation algorithm, and follow by the maximum likelihood estimation approach, which enables us to derive the estimators of parameters involved in this model. We will also present the simulation outcomes to illustrate the efficiency and reliability of the proposed method.

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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 consistent forward rate curves: a tool to estimate and model dynamically the term structure

Cited by 21 publications

References 23 publications

A Note on the Relation Between Principal Components and Dynamic Factors in Affine Term Structure Models

A Note on the Relation Between Principal Components and Dynamic Factors in Affine Term Structure Models

Maximum Likelihood Estimation With Dynamic Measurement Errors and Application to Interest Rate Modeling

A mixed integer linear programming model for optimal sovereign debt issuance

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