A question for anyone studying for the UK ST9 exam for CAS CERA (or fellowship in the Institute & Faculty for that matter). Thankfully I know what TVaR is; I use it on a regular basis when performing analyses. However, I'm not familiar with what Sweeting means by on page 398, equation 15.16, when discussing empirical TVaR through interpolation (it's also page 14 of ST-9 10 in the ActEd Course Notes). The entire equation is: The idea is that you start the standard "Sum and count" from the first "instance" above the cutoff Ta, and then you add the portion of the loss or event that "bled into" the cutoff. So the denominator is adding the "fractional" indication. If I understand the theory, the numerator should add the same fraction of the loss that started below the cutoff, L(x, t-). So is it as simple as Ceiling(Ta) = t+ or am I missing something? Also, I believe this site would greatly benefit from MathJax. Thank you.
Hi - Thanks, I'll take a look at the formula, but meanwhile, note the footnote on p393 of Sweeting where he points out that the exact manner of interpolation is not of great concern. This is certainly an area where the appearance of accuracy may provide undue comfort to the users to these numbers. The examiners recognised this in the September 2011 exam, stating "Candidates are awarded marks for all reasonable answers including different but still reasonable numerical solutions". Specifically, any reasonable approaches to interpolation in the calculation of TVaR in Q8 would have been given credit.
