You can use correct sensitivities … but only if you prove they are close enough to the wrong ones!

The blog's title may seems a little bit cryptic. It is how I feel after ready the long expected FAQ of the BCBS on some issues related to the FRTB. The BCBS document is available on the BIS web site: https://www.bis.org/bcbs/publ/d395.pdf

Before going to the explanation of the title itself, a little bit of history is required. In December 2014, the BCBS published a document on "Fundamental review of the trading book: outstanding issues" and welcomed comments on the proposal. I send my comments to the Committee in February 2015. The comments to the Committee, including mine, have been published on the BIS website shortly after: http://www.bis.org/bcbs/publ/comments/d305/overview.htm. I have commented on the issues in several of my blogs, the first one is Commenting on the Fundamental Review of the Trading Book from March 2015.

The first item on my comments was related to "Computation method for PV01". The original BCBS text was:

My suggestion, after some technical explanation was to
- Rephrase point 20 to require the sensitivity to be computed as the partial derivative, in the mathematical sense, of the instrument value with respect to the relevant rate.
- Leave the implementation and approximation choices on how to compute those numbers to the implementing institutions.
- Potentially mention the formula proposed in the current draft as an acceptable implementation choice.

Now, after roughly two years, the answer of the BCBS is:

Let me rewrite that with my own adaptation of the sentences in square brackets: "a bank may make use of [correct] formulations of sensitivities" instead of the incorrect formulation of the BCBS document, only if the bank can "demonstrate to its supervisor that the [correct] formulations of sensitivities yield results very close to the [incorrect BCBS] formulations".

Wow! I was not expecting such an answer!

Instead of simply indicating that the wording was not perfectly well written and only meant to represent one possible implementation, it keeps the original meaning and tries to indicate that, under the condition of being close to the mandatory definition, the alternative is acceptable according to another part of the text.

The paragraph 47 (c) is by no way meaning what the answer seems to indicate. Paragraph 47 (c) says that it is mandatory to use "sensitivities based on pricing models that the bank’s independent risk control unit uses to report market risks or actual profits and losses to senior management", this obligation is not subordinated to "results very close". Paragraphs 47 (c) and 67/71 are contradicting each other for several banks, but there is no indication in any of them that one can deviate from them, even with "very close results". The FAQ is not an interpretation of the text, it is a new text.

On the other side, what if the two numbers are not close? Which one of those two paragraphs should be violated?

As I'm asking questions, I will also ask the following question: where is the FAQ document question Q1 coming from? In my comments to the Committee, which is, to my knowledge, the first document where the issue was raised, I don't suggest to allow alternative formulation to the Committee one if they are close enough, I suggested to use a standard definition of sensitivity in the sense of derivative and allow for approximation of it. It appears that the question of the approximation and the requirement of the proof have been reversed in the BCBS interpretation of the question asked by the industry. Now banks have to prove that the approximation proposed by the Committee is good enough instead of the more commonsensical reverse approach!

Hopefully the interpretation of those two texts (the original and the FAQ) will mean that in practice common sense will prevail and that both the exact sensitivities (and its AD implementation) and the approximate one sided finite difference sensitivities will be accepted without daily request of a proof.

Note: On another topic, the FAQ mention that it is also allowed to used sticky strike on top of sticky delta for smile treatment. Maybe in the next version they will add sticky moneyness and sticky smile model (like SABR) and we will come closer to actual risk management.

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