# 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 =))

• Calibrate your parameter $\theta(t)$ starting from the forward curve and using the formula in the link above.