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It is well-known that for the calculation of potential future exposure (PFE), real-word probability measure should be used to scenario-generation and risk-neutral measure is used for revaluation; see e.g. J.Hull "Financial Risk Management and Financial Institutions"-chapter 7. Now, the point is how we should go about calibrating real-world parameters, e.g. drift. I know that this task is not obvious. Can anyone explain to me the following points: a) For which classes of risk factor, it is OK to just calibrate drift to historical data, e.g. using simple average? b) For risk factors that are hard to obtain estimates of drift from historical data, what is the best practice to tackle this? Any good reference would be highly appreciated.

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  • $\begingroup$ It is always difficult to estimate the drift of a stochastic process using the sample mean because: (i) financial processes are rarely weakly stationary, (ii) even in the weak stationary case the relative estimation error is not a function of the number of samples but rather of the time period over which the samples were collected, see this answer quant.stackexchange.com/a/25957/19887 $\endgroup$ – Quantuple Aug 31 '17 at 16:50

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