An Efficient Method for Maximum Likelihood Estimation of a Stochastic Volatility Model

• Main Authors: HUANG, Junying, Shirley, YU, Jun
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2008
• Subjects: Finance and Financial Management; Portfolio and Security Analysis
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/1540; https://ink.library.smu.edu.sg/context/lkcsb_research/article/2539/viewcontent/efficientmethod.pdf
• Institution: Singapore Management University

In this paper an efficient, simulation-based, maximumlikelihood (ML) method is proposed for estimating Taylor’sstochastic volatility (SV) model. The new method isbased on the second order Taylor approximation to the integrand.The approximation enables us to transfer the numericalproblem in the Laplace approximation and that inimportance sampling into the problem of inverting two highdimensional symmetric tri-diagonal matrices. A result recentlydeveloped in the linear algebra literature shows thatsuch an inversion has an analytic form, greatly facilitatingthe computations of the likelihood function of the SVmodel. In addition to provide parameter estimation, the newmethod offers an efficient way to filter, smooth, and forecastlatent log-volatility. The new method is illustrated andcompared with existing ML methods using simulated data.Results suggest that the proposed method greatly reducesthe computational cost in estimation without sacrificing thestatistical efficiency, at least for the parameter settings considered.