Saturday, July 28, 2018

stochastic processes - Geometric brownian motion vs. Ornstein Uhlenbeck


I'm looking at the SDE of Geometric brownian motion(*):


dX(t)=σX(t)dB(t)+μX(t)dt


(with analytic solution X(t)=X(0)e(μσ2/2)t+σB(t))


and the SDE of Ornstein-Uhlenbeck process:


dX(t)=σdB(t)+θ(μX(t))dt


In which case the one or the other is better suited for modelling financial data? I read that currrency price data can be well modelled by O-U process. Is there a heuristic/empirical argument for that ?




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