I'm looking at the SDE of Geometric brownian motion(*):
$$d X(t) = \sigma X(t) d B(t) + \mu X(t) d t$$
(with analytic solution $X(t) = X(0) e^{(\mu - \sigma^2 / 2) t + \sigma B(t)}$)
and the SDE of Ornstein-Uhlenbeck process:
$$d X(t) = \sigma d B(t) + \theta (\mu - X(t)) d t$$
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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