2,540 research outputs found
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Linear Gaussian Affine Term Structure Models with Unobservable Factors: Calibration and Yield Forecasting
This paper provides a significant numerical evidence for out-of-sample forecasting ability of linear Gaussian interest rate models with unobservable underlying factors. We calibrate one, two and three factor linear Gaussian models using the Kalman filter on two different bond yield data sets and compare their out-of-sample
forecasting performance. One step ahead as well as four step ahead out-of-sample forecasts are analyzed based on the weekly data. When evaluating the one step ahead forecasts, it is shown that a one factor model may be adequate when only the short-dated or only the long-dated yields are considered, but two and three factor
models performs significantly better when the entire yield spectrum is considered. Furthermore, the results demonstrate that the predictive ability of multi-factor models remains intact far
ahead out-of-sample, with accurate predictions available up to one year after the last calibration for one data set and up to three
months after the last calibration for the second, more volatile data set. The experimental data denotes two different periods with different yield volatilities, and the stability of model
parameters after calibration in both the cases is
deemed to be both significant and practically useful. When it comes to four step ahead predictions, the quality of forecasts deteriorates for all models, as can be expected, but the advantage of using a multi-factor model as compared to a one factor model is still significant.
In addition to the empirical study above, we also suggest a nonlinear filter based on linear programming for improving the term structure matching at a given point in time. This method,
when used in place of a Kalman filter update, improves the term structure fit significantly with a minimal added computational overhead. The improvement achieved with the proposed method is
illustrated for out-of-sample data for both the data sets. This method can be used to model a parameterized yield curve consistently with the underlying short rate dynamics
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Valuation of cash flows under random rates of interest: A linear algebraic approach
This paper reformulates the classical problem of cash flow valuation under stochastic discount factors into a system of linear equations with random perturbations. Using convergence results, a sequence of uniform approximations is developed. The new formulation leads to a general framework for deriving approximate statistics of cash flows for a broad class of models of stochastic interest rate process. We show applications of the proposed method by pricing default-free and defaultable cash flows. The methodology developed in this paper is applicable to a variety of uncertain cash flow analysis problems
Genericness of inflation in isotropic loop quantum cosmology
Non-perturbative corrections from loop quantum cosmology (LQC) to the scalar
matter sector is already known to imply inflation. We prove that the LQC
modified scalar field generates exponential inflation in the small scale factor
regime, for all positive definite potentials, independent of initial conditions
and independent of ambiguity parameters. For positive semi-definite potentials
it is always possible to choose, without fine tuning, a value of one of the
ambiguity parameters such that exponential inflation results, provided zeros of
the potential are approached at most as a power law in the scale factor. In
conjunction with generic occurrence of bounce at small volumes, particle
horizon is absent thus eliminating the horizon problem of the standard Big Bang
model.Comment: 4 pages, revtex4, one figure. Only e-print archive numbers correctedi
in the second version. Reference added in the 3rd version. Final version to
appear in Phys. Rev. Lett. Explanations improve
Reflectionless analytic difference operators I. algebraic framework
We introduce and study a class of analytic difference operators admitting
reflectionless eigenfunctions. Our construction of the class is patterned after
the Inverse Scattering Transform for the reflectionless self-adjoint
Schr\"odinger and Jacobi operators corresponding to KdV and Toda lattice
solitons
Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies
Basic representations of A_{2l}^(2) and D_{l+1}^(2) are studied. The weight
vectors are represented in terms of Schur's -functions. The method to get
the polynomial solutions to the reduced BKP hierarchies is shown to be
equivalent to a certain rule in Maya game.Comment: January 1994, 11 page
Quantum suppression of the generic chaotic behavior close to cosmological singularities
In classical general relativity, the generic approach to the initial
singularity is very complicated as exemplified by the chaos of the Bianchi IX
model which displays the generic local evolution close to a singularity.
Quantum gravity effects can potentially change the behavior and lead to a
simpler initial state. This is verified here in the context of loop quantum
gravity, using methods of loop quantum cosmology: the chaotic behavior stops
once quantum effects become important. This is consistent with the discrete
structure of space predicted by loop quantum gravity.Comment: revtex4, 4 pages, 5 figures. Published version. Title and abstract
changed to match with the published version and Other minor changes.
Conclusions unchange
Absence of the Kasner singularity in the effective dynamics from loop quantum cosmology
In classical general relativity, the generic approach to the initial
singularity is usually understood in terms of the BKL scenario. In this
scenario, along with the Bianchi IX model, the exact, singular, Kasner solution
of vacuum Bianchi I model also plays a pivotal role. Using an effective
classical Hamiltonian obtained from loop quantization of vacuum Bianchi I
model, exact solution is obtained which is non-singular due to a discreteness
parameter. The solution is parameterized in exactly the same manner as the
usual Kasner solution and reduces to the Kasner solution as discreteness
parameter is taken to zero. At the effective Hamiltonian level, the avoidance
of Kasner singularity uses a mechanism distinct from the `inverse volume'
modifications characteristic of loop quantum cosmology.Comment: 4 pages, revtex4, no figure
Pre-classical solutions of the vacuum Bianchi I loop quantum cosmology
Loop quantization of diagonalized Bianchi class A models, leads to a partial
difference equation as the Hamiltonian constraint at the quantum level. A
criterion for testing a viable semiclassical limit has been formulated in terms
of existence of the so-called pre-classical solutions. We demonstrate the
existence of pre-classical solutions of the quantum equation for the vacuum
Bianchi I model. All these solutions avoid the classical singularity at
vanishing volume.Comment: 4 pages, revtex4, no figures. In version 2, reference added and minor
changes made. The final Version 3 includes additional explanation
Discreteness Corrections to the Effective Hamiltonian of Isotropic Loop Quantum Cosmology
One of the qualitatively distinct and robust implication of Loop Quantum
Gravity (LQG) is the underlying discrete structure. In the cosmological context
elucidated by Loop Quantum Cosmology (LQC), this is manifested by the
Hamiltonian constraint equation being a (partial) difference equation. One
obtains an effective Hamiltonian framework by making the continuum
approximation followed by a WKB approximation. In the large volume regime,
these lead to the usual classical Einstein equation which is independent of
both the Barbero-Immirzi parameter as well as . In this work we
present an alternative derivation of the effective Hamiltonian by-passing the
continuum approximation step. As a result, the effective Hamiltonian is
obtained as a close form expression in . These corrections to the
Einstein equation can be thought of as corrections due to the underlying
discrete (spatial) geometry with controlling the size of these
corrections. These corrections imply a bound on the rate of change of the
volume of the isotropic universe. In most cases these are perturbative in
nature but for cosmological constant dominated isotropic universe, there are
significant deviations.Comment: Revtex4, 24 pages, 3 figures. In version 2, one reference and a para
pertaining to it are added. In the version 3, some typos are corrected and
remark 4 in section III is revised. Final version to appear in Class. Quantum
Gra
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