HiDoes anyone know how to estimate the Hull white 1 factor mean reversion parameter(a) in practise? Is it normally done by estimating from the historical data, or calibrated together with the short rate volatility(sigma) from current option prices? I found that when I fixed the mean reversion parameter and estimate the volatility paramter only, the volatilty parameter does not vary much. However, for the same volatility parameter, when changing the maturity of the calibrating options, I got very different mean reversion parameters.Any reference or ideas are much appreciated.Thanks

in my experience, mean reversions are fitted using swaptions of different tenors, either by a root-finding technique (2-d optimisation on vol and MR), or by a trader deciding on a "sensible" mean reversion level.

We have fairly extensive discussion on the role of mean reversion in Sec 13.1.8 (Mean Reversion Calibration) of our bookVladimir

- Cuchulainn
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QuoteOriginally posted by: piterbargWe have fairly extensive discussion on the role of mean reversion in Sec 13.1.8 (Mean Reversion Calibration) of our bookVladimirIs there info on calibration in conjunction with the finite difference method, for example Crank Nicolson or Kolmogorov equation?

Last edited by Cuchulainn on December 2nd, 2010, 11:00 pm, edited 1 time in total.

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There is some in the context of general short rate models; see Section 11.3

there is a thread in the wilmott forums on this subject :http://www.wilmott.com/messageview.cfm? ... d=32285you may be interested in Calibration Methods of Hull-White Modelif you choose the Levenberg Marquardt optimization method, you can find some help to code, here : http://www.quantcode.com/modules/mydown ... hp?lid=522

Thanks all for the messages, very helpful indeed.I tried joint calibration with the mean reversion and volatility parameters, and got a negative value of the mean reversion parameter. Should I in this case prefix the mean reversion parameter and calibrate the volatility parameter only? If so, is it more common to estimate the mean reversion parameter from historical data or otherwise? If it is estimated from historical data, how many days or months data should I include in the consideration?Many thanks for any suggestions.