Approximate Maximum Likelihood Estimation for Diffsuion Processes

• Activity Number: 658
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Song X. Chen*+ and Jing-Yuan Chang
• Companies: Iowa State University/Peking University and Peking University
• Keywords: Diffusion process ; parameter estimation

Abstract

Diffusion processes are commonly employed in modeling the dynamics of financial assets. Despite their popularity and despite their being Markovian, the transitional density functions of these processes are generally not analytically available. This prevents direct usage of the maximum likelihood estimation (MLE). Ait-Sahalia (1998, JF; 2002 Econometrica) proposed Edgeworth type approximations to the transitional densities, which are then used for obtaining approximate MLE. In this paper, we study statistical properties of the approximate maximum likelihood estimators (AMLE) for parametric diffusion processes . The roles of the number of terms used in the approximation and the sampling length are highlighted.