TY - JOUR
AU - Lubrano, Michel
AB - 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 OrnsteinUhlenbeck (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 specificationsmay 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 parametricmodels 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 JoeClayton copula. We find evidence of asymmetric dependence between the two rates, and thatthe level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12)
TI - Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations
JF - Journal of Financial Econometrics
DO - 10.1093/jjfinec/nbq022
DA - 2011-06-30
UR - https://www.deepdyve.com/lp/oxford-university-press/modeling-multivariate-interest-rates-using-time-varying-copulas-and-71h03CXLt0
SP - 198
EP - 236
VL - 9
IS - 1
DP - DeepDyve
ER -