257,206 research outputs found
Boundary energy of the open XXX chain with a non-diagonal boundary term
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain
with a non-diagonal boundary term using a recently proposed Bethe ansatz
solution. As the coefficient of the non-diagonal boundary term tends to zero,
the Bethe roots split evenly into two sets: those that remain finite, and those
that become infinite. We argue that the former satisfy conventional Bethe
equations, while the latter satisfy a generalization of the Richardson-Gaudin
equations. We derive an expression for the leading correction to the boundary
energy in terms of the boundary parameters.Comment: 10 pages, 9 figures; v2: Figs 4 are improved; v3: reference added;
v4: erratum adde
Twisting singular solutions of Bethe's equations
The Bethe equations for the periodic XXX and XXZ spin chains admit singular
solutions, for which the corresponding eigenvalues and eigenvectors are
ill-defined. We use a twist regularization to derive conditions for such
singular solutions to be physical, in which case they correspond to genuine
eigenvalues and eigenvectors of the Hamiltonian.Comment: 10 pages; v2: references added; v3: introduction expanded, and more
references adde
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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
Algebraic Bethe ansatz for singular solutions
The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with
N sites have solutions containing i/2, -i/2 that are singular: both the
corresponding energy and the algebraic Bethe ansatz vector are divergent. Such
solutions must be carefully regularized. We consider a regularization involving
a parameter that can be determined using a generalization of the Bethe
equations. These generalized Bethe equations provide a practical way of
determining which singular solutions correspond to eigenvectors of the model.Comment: 10 pages; v2: refs added; v3: new section on general singular
solutions, and more reference
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