On Stiffness in Affine Asset Pricing Models

24 Pages Posted: 28 Feb 2005

See all articles by Shirley J. Huang

Shirley J. Huang

Singapore Management University - Lee Kong Chian School of Business

Jun Yu

Singapore Management University - School of Economics; Singapore Management University - Lee Kong Chian School of Business

Multiple version iconThere are 2 versions of this paper

Date Written: December 2004

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 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.

Keywords: Affine asset pricing, Characteristic function, Numerical efficiency, Ricatti equations, Explicit and implicit methods, Ordinary differential equations, A-stability

JEL Classification: C13, C32, G12

Suggested Citation

Huang, Shirley J. and Yu, Jun, On Stiffness in Affine Asset Pricing Models (December 2004). Available at SSRN: https://ssrn.com/abstract=676203 or http://dx.doi.org/10.2139/ssrn.676203

Shirley J. Huang

Singapore Management University - Lee Kong Chian School of Business ( email )

469 Bukit Timah Road
Singapore 912409
Singapore

Jun Yu (Contact Author)

Singapore Management University - School of Economics ( email )

90 Stamford Road
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Singapore
+6568280858 (Phone)
+6568280833 (Fax)

HOME PAGE: http://www.mysmu.edu/faculty/yujun/

Singapore Management University - Lee Kong Chian School of Business ( email )

469 Bukit Timah Road
Singapore 912409
Singapore