Calibration of mean reversion models

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Calibration of mean reversion models

lestat

>

>
> Hi, all,
>
> I'm looking for  some model for financial prices that can incorporate random walk and mean reversion. possible candicates include geometric O-U process, the question is how to
> calibrate a geometric O-U process to historical data (I have seen the calibration of O-U, but it's not the same for geometric OU) ? the second question  is when people model mean reversion, they sometimes  fit O-U process to data , however, since most of financial time series are nonstationary (with unit root), how can it be possible to fit a stationary model like OU to nonstationary processes? in particular, when they estimate it, they simply regress delta Xt on Xt which is essentially a linear regression of a stationary process on nonstationary one, what is the rational for this? am I missing sth here?
>
> Thanks!
> Paul Jin
>
>

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Re: Calibration of mean reversion models

Arun.stat
Hi Chenchen, you said "most of financial time series are nonstationary (with unit root), how can it be possible to fit a stationary model " -------- I think it is mostly a matter of taste on what you really believe. Most of the cases (perhaps all) unit root tests are less powerful near the upper boundary of stability region. Therefore although you can not reject of the existence of unit root based on a typical realization, actual DGP may be stationary. Therefore relying heavily on statistical tests may be disastrous. Therefore if you really believe there is some mean-reversion in the actual DGP, you can just go ahead.

Thanks,

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Arun Kumar Saha, FRM
QUANTITATIVE RISK AND HEDGE CONSULTING SPECIALIST
Visit me at: http://in.linkedin.com/in/ArunFRM
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