# why calibrate volatility and fix the mean reversion

I have had a few experiences or chats with teammates about the Hull-White model.

The famous model has 2 parameters :

• The volatility
• The mean reversion

Very often I hear that the mean reversion has been fixed and that the calibration is only done on the volatility.

Why do that ? Why not fix the volatility and optimize on the mean reversion since both parameters have influence on the vanilla products ?

Moreover, why no optimize on both parameters simultaneously ?

Thanks a lot in advance for the context or opinions that help me to understand what are the justification of these practices.

• For a given MR $\lambda$ you calibrate $\sigma(t)$ to coterminal europeans and then price the bermuda. So now your bermuda price is $\text{bermuda} = f(\lambda, \text{coterminals})$. you can then calibrate $\lambda$ to quoted bermudas if there are some. If you are a market maker you can choose the $\lambda$ which you believe in... – Antoine Conze Feb 14 '19 at 15:15