On stiffness in affine asset pricing models

Shirley J. Huang, Jun Yu

Abstract

ABSTRACT

Economic and econometric analysis of continuous-time affine asset pricing models often necessitates solving systems of ordinary differential equations (ODEs) numerically. Explicit Runge–Kutta (ERK) methods have been suggested to solve these ODEs both in the theoretical finance literature and in the 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 ERK 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 performance of these implicit methods relative to certain widely used ERK methods are examined in the context of bond pricing and parameter estimation. The results show that the implicit methods greatly improve the numerical efficiency.