I would like to calibrate Hull-White model using volatility data.I am using [Park (2004)] paper as a reference.
He suggests to minimize the following objective function:
where the first term is theoretical (H-W) conditional volatility [st. dev.] of changes of the spot rates and the second term is defined as:
which is sample variance of observed market data.
My question is:
- why do we subtract variance from volatility[standard deviation] in the objective function? (i.e. not variance - variance).
NOTE: Initially, I thought this was a mistake, but the same expression is used for the two factor model as well (formula (158) in the paper). In addition, I tried to calibrate the model using both (standard deviation - variance) and (standard deviation - standard-deviation) approaches. It seems like the results from (standard deviation-variance) case, as in Park(2004), make more sense.