An Efficient Calibration for One-Factor Short Interest Rate Model

Abstract

Regularization method is popular for solving inverse problems since this method is developed to construct a stable approximate solution for an ill-posed problem. In this paper, this method is applied to the estimation of parameters in one-factor Gaussian interest model and squared Gaussian model with constrained condition. By the variational principle, we derive the corresponding Euler equation and variational inequality for original unconstrained and constrained optimization problem via the regularization method respectively. By using the penalty method, the latter is transformed into a nonlinear two-point boundary value problem, which can be approximated by the usual finite difference numerical method. Stability and convergence analysis are presented. Numerical tests are coincided with theoretical analysis. Finally, we also compare the estimated parameters obtained by using the Gaussian model with those obtained by using squared Gaussian model on test and empirical examples respectively.