Hi David,

This is related to Operational VAR topic.i was not able to get clear picture of what the author was trying to say in closed form solution AIM.here are my doubts:

1How from the equation for analytical model it is implied that The operational VaR (OpVar) at high confidence levels only depends on the tail and not on the body of the severity distribution.

2.Because the frequency enters only as an expectation, it is also not necessary to calibrate
a specific counting process; estimation of the sample mean is sufficient. what does that mean is we need the mean of any frequency distribution like possion for calculation of VAR?

Anil

Hi Anil,

Strong questions. You noted, I am sure, that this reading is concerned with finding *analytical approximations* for a problem that ultimately requires a numerical solution; e.g., The Deutche Bank LDA solves this “numerically.” Even though they dismiss frequency distribution as much less important than severity, they do not go so far as to use only the mean of the frequency distribution. So, the context here is: *approximation* is the price implied by the pursuit of *convenient* analytical solution (the math solves for x tending to infinity; i.e., the formulas are not strictly accurate with realistic datasets). (I am using “analytical” = “closed form”, though they aren’t exactly the same). That said,

1. Mathematically, it’s difficult but virtually according to the premise of operating at the bounds. See how the author gets from F() in formula (2); i.e., the severity distribution...to (3) a function of the “asymptotic” severity function in (3)? But it’s easier to visualize. Think of the standard normal inverse: =NORMSINV(). If you know you are sampling only in the tail, you don’t really care how the body shapes out

2. Yes, only per this analytical approximation. As in (2), only EN(t) the expected (average) frequency enters.

David