Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates

Reducible diffusions (RDs) are nonlinear transformations of analytically solvable Basic Diffusions (BDs). Hence, by construction RDs are analytically tractable and flexible diffusion processes. Existing literature on RDs has mostly focused on time-homogeneous transformations, which to a significant extent fail to explore the full potential of RDs from both theoretical and practical points of view. In this paper, we propose flexible and economically justifiable time variations to the transformations of RDs. Concentrating on the Constant Elasticity Variance (CEV) RDs, we consider nonlinear dynamics for our time-varying transformations with both deterministic and stochastic designs. Such time variations can greatly enhance the flexibility of RDs while maintaining sufficient tractability of the resulting models. In the meantime, our modeling approach enjoys the benefits of classical inferential techniques such as the Maximum Likelihood (ML). Our application to the UK and the US short-term interest rates suggests that from an empirical point of view time-varying transformations are highly relevant and statistically significant. We expect that the proposed models can describe more truthfully the dynamic time-varying behavior of economic and financial variables and potentially improve out-of-sample forecasts significantly.

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.

Cyclosporin A and short-term methotrexate versus cyclosporin A as graft versus host disease prophylaxis in patients with severe aplastic anemia given allogeneic bone marrow transplantation from an HLA-identical sibling:results of a GITMO/EBMT randomized trial

A randomized trial was carried out comparing cyclosporin A (CsA) and short-term methotrexate (MTX) versus CsA alone for graft versus host disease (GVHD) prophylaxis in patients with severe aplastic anemia (SAA) undergoing allogeneic bone marrow transplantation (BMT) from a compatible sibling. Seventy-one patients (median age, 19 years; range, 4-46 years) were randomized to receive either CsA and MTX or CsA alone for the first 3 weeks after BMT. Subsequently, both groups received CsA orally, with gradual drug reduction until discontinuation 8 to 12 months after BMT. Patients randomized in both arms had comparable characteristics and received the same preparative regimen (ie, cyclophosphamide 200 mg/kg over 4 days). The median time for neutrophil engraftment was 17 days (range, 11-31 days) and 12 days (range, 4-45 days) for patients in the CsA/MTX group and the CsA alone group, respectively (P =.01). No significant difference was observed in the probability of either grade 2, grade 3, or grade 4 acute GVHD or chronic GVHD developing in the 2 groups. The Kaplan-Meier estimates of 1-year transplantation-related mortality rates for patients given either CsA/MTX or CsA alone were 3% and 15%, respectively (P =.07). With a median follow-up of 48 months from BMT, the 5-year survival probability is 94% for patients in the CsA/MTX group and 78% for those in the CsA alone group (P =. 05). These data indicate that the use of CsA with MTX is associated with improved survival in patients with SAA who receive transplants from compatible siblings. (Blood. 2000;96:1690-1697)

Effects of short-term chemical ablation of the GIP receptor on insulin secretion, islet morphology and glucose homeostasis in mice

Glucosedependent insulinotropic polypeptide (GIP) is an incretin hormone secreted by endocrine Kcells in response to nutrient absorption. In this study we have utilized a specific and enzymatically stable GIP receptor antagonist, (Pro(3))GIP, to evaluate the contribution of endogenous GIP to insulin secretion and glucose homeostasis in mice. Daily injection of (Pro(3))GIP (25 nmol/kg body weight) for 11 days had no effect on food intake or body weight. Nonfasting plasma glucose concentrations were significantly raised (p