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.

From the UV to the static-field limit: rates and scaling laws of intense-field ionization of helium

We present high-accuracy calculations of ionization rates of helium at UV (195 nm) wavelengths. The data are obtained from full-dimensionality integrations of the helium-laser time-dependent Schrödinger equation. Comparison is made with our previously obtained data at 390 nm and 780 nm. We show that scaling laws introduced by Parker et al extend unmodified from the near-infrared limit into the UV limit. Static-field ionization rates of helium are also obtained, again from time-dependent full-dimensionality integrations of the helium Schrödinger equation. We compare the static-field ionization results with those of Scrinzi et al and Themelis et al, who also treat the full-dimensional helium atom, but with time-independent methods. Good agreement is obtained.

Glucose lowers the threshold for human aortic vascular smooth muscle cell migration: inhibition by protein phosphatase-2A

AIMS/HYPOTHESIS: Atherosclerosis, which occurs prematurely in individuals with diabetes, incorporates vascular smooth muscle cell (VSMC) chemotaxis. Glucose, through protein kinase C-beta(II) signalling, increases chemotaxis to low concentrations of platelet-derived growth factor (PDGF)-BB. In VSMC, a biphasic response in PDGF-beta receptor (PDGF-betaR) level occurs as PDGF-BB concentrations increase. The purpose of this study was to determine whether increased concentrations of PDGF-BB and raised glucose level had a modulatory effect on the mitogen-activated protein kinase/extracellular-regulated protein kinase pathway, control of PDGF-betaR level and chemotaxis.

METHODS: Cultured aortic VSMC, exposed to normal glucose (NG) (5 mmol/l) or high glucose (HG) (25 mmol/l) in the presence of PDGF-BB, were assessed for migration (chemotaxis chamber) or else extracted and immunoblotted.

RESULTS: At concentrations of PDGF-BB <540 pmol/l, HG caused an increase in the level of PDGF-betaR in VSMC (immunoblotting) versus NG, an effect that was abrogated by inhibition of aldose reductase or protein kinase C-beta(II). At higher concentrations of PDGF-BB (>540 pmol/l) in HG, receptor level was reduced but in the presence of aldose reductase or protein kinase C-beta(II) inhibitors the receptor levels increased. It is known that phosphatases may be activated at high concentrations of growth factors. At high concentrations of PDGF-BB, the protein phosphatase (PP)2A inhibitor, endothall, caused an increase in PDGF-betaR levels and a loss of biphasicity in receptor levels in HG. At higher concentrations of PDGF-BB in HG, the chemoattractant effect of PDGF-BB was lost (chemotaxis chamber). Under these conditions inhibition of PP2A was associated with a restoration of chemotaxis to high concentrations of PDGF-BB.

CONCLUSION/INTERPRETATION: The biphasic response in PDGF-betaR level and in chemotaxis to PDGF-BB in HG is due to PP2A activation.