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17
Forecasting the term structure of government bond yields
 Journal of Econometrics
, 2006
"... Despite powerful advances in yield curve modeling in the last twenty years, comparatively little attention has been paid to the key practical problem of forecasting the yield curve. In this paper we do so. We use neither the noarbitrage approach, which focuses on accurately fitting the cross sectio ..."
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Cited by 133 (12 self)
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Despite powerful advances in yield curve modeling in the last twenty years, comparatively little attention has been paid to the key practical problem of forecasting the yield curve. In this paper we do so. We use neither the noarbitrage approach, which focuses on accurately fitting the cross section of interest rates at any given time but neglects timeseries dynamics, nor the equilibrium approach, which focuses on timeseries dynamics (primarily those of the instantaneous rate) but pays comparatively little attention to fitting the entire cross section at any given time and has been shown to forecast poorly. Instead, we use variations on the NelsonSiegel exponential components framework to model the entire yield curve, periodbyperiod, as a threedimensional parameter evolving dynamically. We show that the three timevarying parameters may be interpreted as factors corresponding to level, slope and curvature, and that they may be estimated with high efficiency. We propose and estimate autoregressive models for the factors, and we show that our models are consistent with a variety of stylized facts regarding the yield curve. We use our models to produce termstructure forecasts at both short and long horizons, with encouraging results. In particular, our forecasts appear much more accurate at long horizons than various standard benchmark forecasts. Finally, we discuss a number of extensions, including generalized duration measures, applications to active bond portfolio management, and arbitragefree specifications. Acknowledgments: The National Science Foundation and the Wharton Financial Institutions Center provided research support. For helpful comments we are grateful to Dave Backus, Rob Bliss, Michael Brandt, Todd Clark, Qiang Dai, Ron Gallant, Mike Gibbons, Da...
Asset Pricing Under The Quadratic Class
 Journal of Financial and Quantitative Analysis
, 2002
"... We identify and characterize a class of term structure models where bond yields are quadratic functions of the state vector. We label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application. We consider asset pricing in general and derivative ..."
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Cited by 36 (6 self)
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We identify and characterize a class of term structure models where bond yields are quadratic functions of the state vector. We label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application. We consider asset pricing in general and derivative pricing in particular under the quadratic class. We provide two general transform methods in pricing a wide variety of fixed income derivatives in closed or semiclosed form. We further illustrate how the quadratic model and the transform methods can be applied to more general settings. # Swiss Banking Institute, University of Zurich, Plattenstr. 14, 8032 Zurich, Switzerland and Graduate School of Business, Fordham University, 113 West 60th Street, New York, NY 10023, USA, respectively. We thank Marco Avellaneda, David Backus, Peter Carr, Pierre Collin, Silverio Foresi, Michael Gallmeyer, Richard Green, Massoud Heidari, Burton Hollifield, Regis Van Steenkiste, Chris Telmer, Stanley Zin, and, in particular, Jonathan M. Karpo# (the editor) as well as two anonymous referees for helpful comments. I.
A Note On The NelsonSiegel Family
"... . We study a problem posed in Bjork and Christensen (1999): does there exist any nontrivial interest rate model which is consistent with the NelsonSiegel family? They show that within the HJM framework with deterministic volatility structure the answer is no. In this paper we give a generalized ve ..."
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Cited by 25 (0 self)
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. We study a problem posed in Bjork and Christensen (1999): does there exist any nontrivial interest rate model which is consistent with the NelsonSiegel family? They show that within the HJM framework with deterministic volatility structure the answer is no. In this paper we give a generalized version of this result including stochastic volatility structure. For that purpose we introduce the class of consistent state space processes, which have the property to provide an arbitragefree interest rate model when representing the parameters of the NelsonSiegel family. We characterize the consistent state space Ito processes in terms of their drift and di#usion coe#cients. By solving an inverse problem we find their explicit form. It turns out that there exists no nontrivial interest rate model driven by a consistent state space Ito process. 1. Introduction Bjork and Christensen (1999) introduce the following concept: let M be an interest rate model and G a parameterized family o...
Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates?
 Journal of Fixed Income
, 2001
"... We investigate whether the same finite dimensional dynamic system spans both interest rates (the yield curve) and interest rate options (the implied volatility surface). We find that the options market exhibits factors independent of the underlying yield curve. While three common factors are adeq ..."
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Cited by 22 (4 self)
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We investigate whether the same finite dimensional dynamic system spans both interest rates (the yield curve) and interest rate options (the implied volatility surface). We find that the options market exhibits factors independent of the underlying yield curve. While three common factors are adequate to capture the systematic movement of the yield curve, we need three additional factors to capture the movement of the implied volatility surface. JEL Classification Codes: E43, G12. Key Words: Factors; principal component; LIBOR; swaps; swaptions; yield curve; implied volatility surface. We measure and interpret common factors underlying the US dollar LIBOR market that includes both interest rates and interest rate options. In particular, we investigate whether the same finite dimensional dynamic system spans both types of instruments. We find that the options market exhibits factors independent of the underlying yield curve. We identify three common factors from LIBOR and swap rat...
HJM: A Unified Approach to Dynamic Models for Fixed Income, Credit and Equity Markets
"... Summary. The purpose of this paper is to highlight some of the key elements of the HJM approach as originally introduced in the framework of fixed income market models, to explain how the very same philosophy was implemented in the case of credit portfolio derivatives and to show how it can be exten ..."
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Cited by 5 (5 self)
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Summary. The purpose of this paper is to highlight some of the key elements of the HJM approach as originally introduced in the framework of fixed income market models, to explain how the very same philosophy was implemented in the case of credit portfolio derivatives and to show how it can be extended to and used in the case of equity market models. In each case we show how the HJM approach naturally yields a consistency condition and a noarbitrage conditions in the spirit of the original work of Heath, Jarrow and Morton. Even though the actual computations and the derivation of the drift condition in the case of equity models seems to be new, the paper is intended as a survey of existing results, and as such, it is mostly pedagogical in nature. 1
Invariant manifolds for weak solutions to stochastic equations
 Probability Theory & Related Fields , Volume 118 (2000), Number 3. 323
"... Abstract. Viability and invariance problems related to a stochastic equation in a Hilbert space H are studied. Finite dimensional invariant C2 submanifolds of H are characterized. We derive Nagumo type conditions and prove a regularity result: Any weak solution, which is viable in a finite dimension ..."
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Cited by 4 (1 self)
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Abstract. Viability and invariance problems related to a stochastic equation in a Hilbert space H are studied. Finite dimensional invariant C2 submanifolds of H are characterized. We derive Nagumo type conditions and prove a regularity result: Any weak solution, which is viable in a finite dimensional C2 submanifold, is a strong solution. These results are related to finding finite dimensional realizations for stochastic equations. There has recently been increased interest in connection with a model for the stochastic evolution of forward rate curves. 1.
Taking Positive Interest Rates Seriously
 WORKING PAPER, ZICKLIN SCHOOL OF BUSINESS, BARUCH
, 2003
"... We propose a dynamic term structure model where interest rates of all maturities are bounded from below at zero. We show that positivity and continuity, combined with no arbitrage, impose such a tight restriction on the term structure that only one functional form is possible. Even more strikingl ..."
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Cited by 2 (0 self)
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We propose a dynamic term structure model where interest rates of all maturities are bounded from below at zero. We show that positivity and continuity, combined with no arbitrage, impose such a tight restriction on the term structure that only one functional form is possible. Even more strikingly, the term structure is governed by exactly three sources of risk, only one of which is dynamic. This one dynamic source controls the level of the interest rate and follows a special twoparameter square root process under the riskneutral measure. The two parameters of the process determine the other two sources of risk and can be regarded as two static factors. Thus, unlike traditional models, this has no other parameters to estimate and hence no other risks to bear. We cast the model into a state space framework and estimate the model on both U.S. Treasury yields and U.S. dollar swap rates. Despite its extreme simplicity, the model fits the term structures of both markets well. The pricing errors are mostly within a few basis points.
Time in Yrs Annual Coupon Market Price
"... The ordinary bootstrap method for computing forward rates from zero rates generates posynomial equations as introduced in an area of optimization termed geometric programming invented by Duffin, Peterson, and Zener [6]. posynomial disc. fns e−zk(tk−t0) �k−1 = i=0 x (ti+1−ti) i,i+1, k = 1,... express ..."
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The ordinary bootstrap method for computing forward rates from zero rates generates posynomial equations as introduced in an area of optimization termed geometric programming invented by Duffin, Peterson, and Zener [6]. posynomial disc. fns e−zk(tk−t0) �k−1 = i=0 x (ti+1−ti) i,i+1, k = 1,... express the forward rates zk(tk − t0) = � k−1 i=0 fi,i+1(ti+1 − ti), where xi,i+1 = e −fi,i+1 in Tables 2–4. Note that the are n equations in m unknowns (n = m =5). Ordinary bootstrapping does not work when n � = m, eg., if there were no 0.5 time T–Bill. 1 (1)
ON FINITEDIMENSIONAL TERM STRUCTURE MODELS DAMIR FILIPOVIĆ AND JOSEF TEICHMANN
"... Abstract. In this paper we provide the characterization of all finitedimensional Heath–Jarrow–Morton models that admit arbitrary initial yield curves. It is well known that affine term structure models with timedependent coefficients (such as the Hull–White extension of the Vasicek short rate mode ..."
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Abstract. In this paper we provide the characterization of all finitedimensional Heath–Jarrow–Morton models that admit arbitrary initial yield curves. It is well known that affine term structure models with timedependent coefficients (such as the Hull–White extension of the Vasicek short rate model) perfectly fit any initial term structure. We find that such affine models are in fact the only finitefactor term structure models with this property. We also show that there is usually an invariant singular set of initial yield curves where the affine term structure model becomes timehomogeneous. We also argue that other than functional dependent volatility structures – such as local state dependent volatility structures – cannot lead to finitedimensional realizations. Finally, our geometric point of view is illustrated by several examples. 1.
Handbook of Mathematical Finance,
, 2000
"... Cambridge University Press The purpose of this essay is to give an overview of some recent work concerning structural properties of the evolution of the forward rate curve in an arbitrage free bond market. The main problems to be discussed are as follows. • When is a given forward rate model consist ..."
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Cambridge University Press The purpose of this essay is to give an overview of some recent work concerning structural properties of the evolution of the forward rate curve in an arbitrage free bond market. The main problems to be discussed are as follows. • When is a given forward rate model consistent with a given family of forward rate curves? • When can the inherently infinite dimensional forward rate process be realized by means of a finite dimensional state space model. We consider interest rate models of HeathJarrowMorton type, where the forward rates are driven by a multidimensional Wiener process, and where he volatility is allowed to be an arbitrary smooth functional of the present forward rate curve. Within this framwork we give necessary and sufficient conditions for consistency, as well as for the existence of a finite