Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Energy levels and radiative rates for transitions in Ni XIII-Ni XVI

Energy levels and radiative rates for fine-structure transitions in nickel ions (Ni XIII-XVI) have been calculated using the GRASP code. Configuration interaction and relativistic effects have been included, and comparisons are made with available data. Energy levels and radiative rates are tabulated for transitions among the 48, 43, 32, and 84 levels of Ni XIII, Ni XIV, Ni XV, and Ni XVI, respectively. The energy levels are assessed to be accurate to better than 5% for a majority of levels, while oscillator strengths for all strong transitions are accurate to better than 20%. (C) 2003 Published by Elsevier Inc.

Energy levels and radiative rates for transitions in Ar XIII, Ar XIV and Ar XV

Energies for 524 levels of Ar XIII, 460 levels of Ar XIV and 156 levels of Ar XV have been calculated using the GRASP code of Dyall et al. (1989). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Comparisons are made with the limited results available in the literature, and the accuracy of the data is assessed. Our energy levels are estimated to be accurate to better than 1%, whereas results for other parameters are probably accurate to better than 20%. Additionally, the level lifetimes derived from our radiative rates are in excellent agreement with measured values.

Electron impact excitation of Gd XXXVII and radiative rates for Ni-like ions with 60

Energy levels and radiative rates for transitions among the 107 finestructure levels belonging to the (1s(2)2s(2)2p(6)) 3s(2)3p(6)3d(10), 3s(2)3p(6)3d(9)4l, 3s(2)3p(5)3d(10)4l, and 3s3p(6)3d(10)4l configurations of Ni-like ions with 60 less than or equal to Z less than or equal to 90 have been calculated using the GRASP code. The collision strengths (Omega) have also been computed for transitions in Gd XXXVII at energies below 800 Ryd, using the DARC code. Resonances have been resolved in a fine energy mesh in the threshold region, and excitation rate coefficients have been calculated for transitions from the ground level to excited levels at temperatures below 2500 eV. These have been compared with those available in the literature, and enhancement in the values of rates, due to resonances, has been observed up to an order of magnitude for some of the transitions.

Energy levels and radiative rates for Li-like Ar XVI and Fe XXIV

Energy levels for transitions among the lowest 24 fine- structure levels belonging to the 1s(2)nl(n greater than or equal to 5) configurations of Li-like Ar XVI and Fe XXIV have been calculated using the fully relativistic GRASP code. Oscillator strengths, radiative rates and line strengths have also been generated among these levels for the four types of transitions: electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2) and magnetic quadrupole (M2). Comparisons are made for the electric dipole transitions with other available results, and the accuracy of the present data is assessed.

Electron impact excitation of Fe XVI: radiative and excitation rates

Aims. In this paper we report calculations for energy levels, radiative rates, collision strengths, and effective collision strengths for transitions in Fe XVI. Methods. For energy levels and radiative rates we have used the General purpose Relativistic Atomic Structure Package ( grasp), and for the compuations of collision strengths the Dirac Atomic R-matrix Code (darc) has been adopted. Results. Energies for the lowest 39 levels among the n

Energy levels, radiative rates, and excitation rates for transitions in OIV

Aims. In this paper we report calculations for energy levels, radiative rates, and excitation rates for transitions in O IV. Methods. The grasp (general-purpose relativistic atomic structure package) and FAC (flexible atomic code) were adopted for calculating energy levels and radiative rates, and the Dirac atomic R-matrix code (DARC) used to determine the excitation rates. Results. Oscillator strengths and radiative rates are reported for all E1, E2, M1, and M2 transitions among the lowest 75 levels of O IV. Additionally, lifetimes are reported for all levels and comparisons made with those available in the literature. Finally, effective collision strengths are reported for all transitions over a wide temperature range below 106 K. Comparisons are made with earlier results and the accuracy of the data is assessed.

Energy levels and radiative rates for transitions in B-like to F-like Kr ions (Kr XXXII-XXVIII)

Energy levels, radiative rates, oscillator strengths, line strengths, and lifetimes have been calculated for transitions in B-like to F-like Kr ions, Kr XXXIII-XXVIII. For the calculations, the fully relativistic GRASP code has been adopted, and results are reported for all electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions among the lowest 125, 236, 272, 226, and 113 levels of Kr XXXII, Kr XXXI, Kr XXX, Kr XXIX, and Kr XXVIII, respectively, belonging to the n

Energy levels and radiative rates for transitions in Mg-like iron, cobalt and nickel

Energy levels and radiative rates for electric dipole (E1) transitions among the lowest 141 levels of the (IS2 2s(2) 2P(6)) 3l(2) , 3l3l', and 3l4l configurations of Fe XV, Co XVI, and Ni XVII are calculated through the CIV3 code using extensive configuration-interact ion (CI) wavefunctions. The important relativistic effects are included through the Breit-Pauli approximation. In order to keep the calculated energy splittings close to the experimental values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. The energy levels, including their orderings, are in excellent agreement with the available experimental results for all three ions. However, experimental energies are only available for a few levels. Since mixing among some levels is found to be very strong, it becomes difficult to identify these uniquely. Additionally, some discrepancies with other theoretical work (particularly for Ni XVII) are very large. Therefore, in order to confirm the level ordering as well as to assess the accuracy of energy levels and radiative rates, we have performed two other independent calculations using the GRASP and FAC codes. These codes are fully relativistic, but the CI in the calculations is limited to the basic (minimum) configurations only. This enables us to assess the importance of including elaborate Cl for moderately charged ions. Additionally, we report results for electric quadrupole (E2), magnetic dipole (MI), and magnetic quadrupole (M2) transitions, and list lifetimes for all levels. Comparisons are made with other available experimental and theoretical results, and the accuracy of the present results is assessed. (c) 2007 Elsevier Inc. All rights reserved.

Energy levels, radiative rates and excitation rates for transitions in Ni XI

Aims. In this paper we report calculations for energy levels, radiative rates and excitation rates for transitions in Ni xi.
Methods. The grasp (General-purpose Relativistic Atomic Structure Package) and fac (Flexible Atomic Code) have been adopted
for calculating energy levels and radiative rates, and the Dirac Atomic R-matrix Code (darc) has been used to determine the excitation
rates.
Results. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest
250 levels of Ni xi. Additionally, lifetimes are also reported for all levels. However, results for excitation rates are presented only for
transitions among the lowest 17 levels.

Energy levels and radiative rates for transitions in Co XI

Aims.In this paper we report calculations for energy levels and radiative rates for transitions in Co XI.

Energy levels and radiative rates for transitions in Ni XIX

Aims. In this paper we report calculations for energy levels and radiative rates for transitions in Ni XIX.