Simulated Maximum Likelihood Estimation for Latent Diffusion Models

• Main Authors: KLEPPE, Tore Selland, YU, Jun, SKAUG, Hans J.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2011
• Subjects: Closed-form approximation; Diffusion Model; Efficient importance sampler; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1310; https://ink.library.smu.edu.sg/context/soe_research/article/2309/viewcontent/sml_garchdiffusion01_10_2011.pdf
• Institution: Singapore Management University

In this paper a method is developed and implemented to provide the simulated maximum likelihood estimation of latent diffusions based on discrete data. The method is applicable to diffusions that either have latent elements in the state vector or are only observed at discrete time with a noise. Latent diffusions are very important in practical applications in financial economics. The proposed approach synthesizes the closed form method of Ait-Sahalia (2008) and the efficient importance sampler of Richard and Zhang (2007). It does not require any infill observations to be introduced and hence is computationally tractable. The Monte Carlo study shows that the method works well infinite sample. The empirical applications illustrate usefulness of the method and find no evidence of infinite variance in the importance sampler.