Linda allen and DB' s LDA

[peter333]

Hi David:

I have two questions.

(i) Linda allen chapter 5 (on Page 7 of notes) for income based models says that residual should be interpreted as operational risk. Please correct me, if I am wrong, should not it be alpha? because alpha captures the mean effect of omitted variables and residual is just a stochastic term. Obviously, there can be problems with residual term where it is not stochastic but still defining it as operational risk does not look good to me. It should be alpha.

(ii) On page 25 of ur notes from Boecker reading you say it is not necessary to model the body of severity distribution and modelling the whole distribution function is superflous. Moreover, calibrating the counting process of frequency distribution is not required. While DB's LDA paper strive hard for both of these steps. They model the whole body of severity distribution (page 21-22 of original paper) and also calibrate frequency distribution (parts of section 6). Actually they give these steps full importance. I mean isn't it contradictory? :roll:

best regards,

peter333

 

[David Harper CFA FRM]

Hi Peter,

(i) Nice. I hadn't noticed this, but my first instinct is *total agreement.* The only qualification is: I don't have (nor does Allen give) a detailed resource on income-based model for Operational risk. (Does anyone really do this?) It seems unclear how the regression is used here. My interpretation would be like yours: operational risk, I would think, is attributed to the INTERCEPT in the multivariate model. If so, the intercept = alpha, and the mean residual = 0 where, as you say, the residual collects randomness. Perhaps (?) the method omits the intercept and then the residual commingles alpha and the stochastic residual; but this this would seem to create more problems.


(ii) They are different, but please note the Bocker reading is about a short-hand (analytical) solution to a problem that generally requires a numerical approach as conducted by DB LDA. I view the whole Bocker reading as an expansion on its formula (2): G(x) ~ EN(t)F(x). As in, the true loss distribution, G(x) which is frequency compounded by a severity distribution, is APPROXIMATED BY the mean frequency and the tail severity. So, per the title, it is a "closed form approximation" to what otherwise cannot be solved analytically.

But also please note the DB LDA in 11.1.3 they do refer to Bocker's closed-form approach as valid approach for the conduct of SENSITIVITY analysis. So, they view it a something of a complement (And note it fits thematically with something i'd expect to be tested: that the frequency distribution is less important than the severity distribution)

David

 

[peter333]

Thanks David...nice explanation...I understood that they are different but I missed DB's refernce..so now its clear

best regards,

peter333