I am trying to find some research pertaining to the historical (or real world) calibration of stochastic volatility models.
For example, in applications such as counterparty credit risk (IMM) or economic scenario generators (ESG), it is not unusual to simulate under the historical measure to generate exposures of various risk factors.
It is also clear that the properties exhibited by stochastic volatility models are particularly interesting for long horizon simulation.
I would like to know how one would calibrate the SABR model for example to historical data? I would assume that the model would be fitted independently for each day and the resulting time series of parameters would be fitted with a statistical model.
Finally, what is the consensus (If any) for the applications mentioned above (namely IMM and ESG): do people use the risk neutral calibration instead ?