Publication Type
Working Paper
Version
publishedVersion
Publication Date
10-2010
Abstract
A new algorithm is developed to provide a simulated maximum likelihood estimation of the GARCH diffusion model of Nelson (1990) based on return data only. The method combines two accurate approximation procedures, namely, the polynomial expansion of Ait-Sahalia (2008) to approximate the transition probability density of return and volatility, and the Efficient Importance Sampler (EIS) of Richard and Zhang (2007) to integrate out the volatility. The first and second order terms in the polynomial expansion are used to generate a base-line importance density for an EIS algorithm. The higher order terms are included when evaluating the importance weights. Monte Carlo experiments show that the new method works well and the discretization error is well controlled by the polynomial expansion. In the empirical application, we fit the GARCH diffusion to equity data, perform diagnostics on the model fit, and test the finiteness of the importance weights.
Keywords
Efficient importance sampling, GARC diffusion model, Simulated Maximum likelihood, Stochastic volatility
Discipline
Econometrics | Finance
Research Areas
Econometrics
First Page
1
Last Page
34
Publisher
SMU Economics and Statistics Working Paper Series, No. 13-2010
City or Country
Singapore
Citation
KLEPPE, Tore Selland; YU, Jun; and SKAUG, Hans J..
Estimating the GARCH Diffusion: Simulated Maximum Likelihood in Continuous Time. (2010). 1-34.
Available at: https://ink.library.smu.edu.sg/soe_research/1232
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.