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.

Using simulation to assess cardiac first-responder schemes exhibiting stochastic and spatial complexities

A Monte-Carlo simulation-based model has been constructed to assess a public health scheme involving mobile-volunteer cardiac First-Responders. The scheme being assessed aims to improve survival of Sudden-Cardiac-Arrest (SCA) patients, through reducing the time until administration of life-saving defibrillation treatment, with volunteers being paged to respond to possible SCA incidents alongside the Emergency Medical Services. The need for a model, for example, to assess the impact of the scheme in different geographical regions, was apparent upon collection of observational trial data (given it exhibited stochastic and spatial complexities). The simulation-based model developed has been validated and then used to assess the scheme's benefits in an alternative rural region (not a part of the original trial). These illustrative results conclude that the scheme may not be the most efficient use of National Health Service resources in this geographical region, thus demonstrating the importance and usefulness of simulation modelling in aiding decision making.

A hybrid metaheuristic approach to the university course timetabling problem

This paper describes the development of a novel metaheuristic that combines an electromagnetic-like mechanism (EM) and the great deluge algorithm (GD) for the University course timetabling problem. This well-known timetabling problem assigns lectures to specific numbers of timeslots and rooms maximizing the overall quality of the timetable while taking various constraints into account. EM is a population-based stochastic global optimization algorithm that is based on the theory of physics, simulating attraction and repulsion of sample points in moving toward optimality. GD is a local search procedure that allows worse solutions to be accepted based on some given upper boundary or ‘level’. In this paper, the dynamic force calculated from the attraction-repulsion mechanism is used as a decreasing rate to update the ‘level’ within the search process. The proposed method has been applied to a range of benchmark university course timetabling test problems from the literature. Moreover, the viability of the method has been tested by comparing its results with other reported results from the literature, demonstrating that the method is able to produce improved solutions to those currently published. We believe this is due to the combination of both approaches and the ability of the resultant algorithm to converge all solutions at every search process.

A Search for Line Shape and Depth Variations in 51 Pegasi and tau Bootis

Spectroscopic observations of 51 Pegasi and tau Bootis show no periodic changes in the shapes of their line profiles; these results for 51 Peg are in significant conflict with those reported by Gray & Hatzes. Our detection limits are small enough to rule out nonradial pulsations as the cause of the variability in tau Boo, but not in 51 Peg. The absence of line shape changes is consistent with these stars' radial velocity variability arising from planetary mass companions.

Pulsating or not? A search for hidden pulsations below the red edge of the ZZ Ceti instability strip

The location of the red edge of the ZZ Ceti instability strip is defined observationally as being the lowest temperature for which a white dwarf with a H-rich atmosphere (DA) is known to exhibit periodic brightness variations. Whether this cut-off in flux variations is actually due to a cessation of pulsation or merely due to the attenuation of any variations by the convection zone, rendering them invisible, is not clear. The latter is a theoretical possibility because with decreasing effective temperature, the emergent flux variations become an ever smaller fraction of the amplitude of the flux variations in the interior. In contrast to the flux variations, the visibility of the velocity variations associated with the pulsations is not thought to be similarly affected. Thus, models imply that were it still pulsating, a white dwarf just below the observed red edge should show velocity variations. In order to test this possibility, we used time-resolved spectra of three DA white dwarfs that do not show photometric variability, but which have derived temperatures only slightly lower than the coolest ZZ Ceti variables. We find that none of our three targets show significant periodic velocity variations, and set 95% confidence limits on amplitudes of 3.0, 5.2, and 8.8 km s(-1). Thus, for two out of our three objects, we can rule out velocity variations as large as 5.4 km s(-1) observed for the strongest mode in the cool white dwarf pulsator ZZ Psc. In order to verify our procedures, we also examined similar data of a known ZZ Ceti, HL Tau 76. Applying external information from the light curve, we detect significant velocity variations for this object with amplitudes of up to 4 km s(-1). Our results suggest that substantial numbers of pulsators having large velocity amplitudes do not exist below the observed photometric red edge and that the latter probably reflects a real termination of pulsations.