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Parameter estimation of multiple Geometric BM with Maximum Likelihood
Posted: July 19th, 2004, 4:54 pm
by beata
say we have N firms and their firm value processes are given by correlated Geometric Brownian motionsd V_i_t = V_i_t * (/miu_i) * dt + V_i_t * sum_ j=1:M [/sigma_ij*dW_ j_t ], for i=1:N.I am looking for some REFERENSE which explains how to calculate the parameters of the correlated Geometric Brownian motions given historical data for each firm value V_i_t, and using the maximum likelihood method.thnx
Parameter estimation of multiple Geometric BM with Maximum Likelihood
Posted: July 19th, 2004, 6:40 pm
by obeelde
Beata,Take a look at the following paper by Andrew Lo for the definitive Theory:Maximum Likelihood Estimation of Generalized Ito Processes with Discretely-Sampled Data, Econometric Theory 4(1988), 231-247. In this particular case, the estimation theory is very easy because we know that when we take the natural log transformation we get arithmetic brownian motion which has a normal distribution. In the multivariate case, we end up with a multivariate normal distribution after taking the natural log transformation.RegardsOwen
Parameter estimation of multiple Geometric BM with Maximum Likelihood
Posted: July 19th, 2004, 7:07 pm
by beata
Owen,this paper is not available for free on the Internet.I guess I will have to look for something else.But thanks anyway
Parameter estimation of multiple Geometric BM with Maximum Likelihood
Posted: July 19th, 2004, 8:56 pm
by obeelde
Beata,Look at equation (30) of "Conditional estimation of diffusion processes" by Minqiang Li, Neil D. Pearson,yand Allen M. PoteshmanFor an example of the density for the geometric brownian motion process. Simply generalize to the multivariateOwen