On Stiffness in Affine Asset Pricing Models∗

Economic and econometric analysis of continuous-time affine asset pricing models often necessitates solving systems of ordinary differential equations (ODEs) numerically. Explicit Runge-Kutta methods have been suggested to solve these ODEs in both the theoretical finance and financial econometrics literature. In this paper we show that under many empirically relevant circumstances the ODEs involve stiffness, a phenomenon which leads to some practical difficulties for numerical methods with a finite region of absolute stability, including the whole class of explicit Runge-Kutta methods. The difficulties are highlighted in the present paper in the context of pricing zero coupon bonds as well as econometric estimation of dynamic term structure models via the empirical characteristic function. To overcome the numerical difficulties, we propose to use implicit numerical methods for the ODEs. The performances of these implicit methods relative to certain widely used explicit Runge-Kutta methods are examined in context of bond pricing and parameter estimation. The results show that the implicit methods greatly improve the numerical efficiency.