# Estimation of Geometric Brownian Motion drift

One can find many papers about estimators of the historical volatility of a geometric Brownian motion (GBM). I'm interested in the estimation of the drift of such a process. Any link on this topic would be very helpful.

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One reference is "The Econometrics of Financial Markets" by John Y. Campbell, Andrew W. Lo, & A. Craig MacKinlay -- http://press.princeton.edu/TOCs/c5904.html. In particular:

 9.3.1 Parameter Estimation of Asset Price Dynamics 356
9.3.4 The Effects of Asset Return Predictability 369


You might also take a look at Chan (1992) "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate" which discusses parameter estimation of several models including the GBM: http://rady.ucsd.edu/faculty/directory/valkanov/classes/mfe/docs/Longstaff_JoF_1992.pdf

There are also rather nice packages for R, 'sde' and 'yuima', which allow you (among many other things) to estimate the parameters of the SDE models. Take a look at the slides -- http://www.rinfinance.com/agenda/2011/StefanoIacus.pdf -- in particular, you may find the "Estimation of Financial Models" part quite useful.

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Thank you very much!! –  Juergen Feb 12 '12 at 22:45