# Historical calibration of Hull-White model

I have a question concerning 1-factor Hull-White model. For my master project I need to calibrate it to compute Counterparty credit risk metrics. I know that the model might be calibrated either for risk-neutral measure (in CVA applications) using market-traded swaptions or caps or for historical measure. This is where I am stuck at the moment. Can anyone offer a good paper / or some idea how to calibrate mean reversion parameter a and variance sigma to the historical data? What historical data do I have to use? And how to perform the calibration step-by-step?

If anyone also has also a solution in Matlab and could share it - that would be also highly appreciated =))

Thanks in advance

• have you try using a kalman filter? – Bond007 Mar 29 '17 at 11:49

## 2 Answers

You can find Matlab code in these notes: http://cosweb1.fau.edu/~jmirelesjames/MatLabCode/Lecture_notes_2008d.pdf I wrote them 10 years ago and have not revisited since, but it should work.

I hope you can find the answer to your question here: How to calibrate Hull-White from zero curve? However if you want a step-by-step procedure I would resume it like that:

• Calibrate your parameter $\theta(t)$ starting from the forward curve and using the formula in the link above.
• Calibrate volatility from the historical series of the forward curve
• Similarly estimate the mean reversion speed