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What level of calculus is assumed

jpresmanes

AVP Risk
David, what level of calculus is assumed for the FRM exam?

Jim Presmanes

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Jim,

Really common question! The test is somewhat quantitative but, on a strict definition of calculus, there is little formal calculus. I just published the first episode and itâ€™s almost not an exaggeration to say the calculus â€œpeaksâ€ in this first episode (with the Taylor Series, which does not need to be derived but rather conceptually appreciated). First and second-order (partial) derivatives are about the extent of the calculus. (and logs and exponential play a role, but I consider that pre-calculus).

If math can be viewed in two dimensions, depth and breadth, the exam is extensively mathematical/quantitative in BREADTH more than DEPTH. Most of the math (e.g., option pricing, credit derivatives, Baselâ€™s IRB, hedge fund metrics) operate at a pre-calc level because they combine mathematical and statistical building blocks. For example, here is a 2008 FRM learning outcome (AIM): "Compute the value of a European option using the Black-Scholes-Merton model on a dividend-paying stock." Calculus is required to understand the derivation of this differential equation, but the FRM does not require that; the FRM requires only application of the BSM which uses building blocks (logs and standard normal cumulative distribution).

To put into another light (I get this quant question often), the new Quant text this year is Essentials of Econometrics (the first eight chapters) and, well, it has 80% overlap with the text it replaced (Statistics) plus a chapter on multiple regression. So, that is all math for sure and but it's really statistics much more than calculus

In short, the exam is significantly quant but that quant is more "econometrics" and pre-calc than calculus.

I hope that helps!

David

jpresmanes

AVP Risk
Thanks, I hope I can ask one more. Does FRM/Bionic Turtle training package present any approaches to modeling low probability, high severity operational loss events?

Thanks, Jim

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Jim,

The bionic turtle follows the FRM curriculum each year, freshly updated, so we don't offer a separate operational loss module. We will cover the new learning outcomes as they pertain to this topic. This happens to be an area GARP has expanded over the last two seasons, clearly it is a focus but at the same time it is not nearly as settled as market & credit risk. The exam reviews a hodge-podge of qualitative (scorecard) approaches and the quant focus is generally loss distribution approaches (LDA):

* There is an (pretty shallow, frankly) intro to extreme value theory (EVT, GEV & GPD distributions to characterize extreme tails)
* Klaus Boecker and Claudia Kluppelberg, 2007,"Operational VaR: a Closed-Form Approximation
* Falko Aue and Michael Kalkbrener, 2007, â€œLDA at Workâ€, Deutsche Bank White Paper. This is the most detailed reading in the 2008 FRM on OpRisk measurement, IMO. This is the one you might take a look at. It's a case study on AMA under Basel II
* As part of the Basel II focus, there is a bit of coverage of the 'advanced' regulatory ADA approach (but it's bullet point type review)

Thanks, David