Differentiating Basel Credit Risk Weights with Respect to MoC C
Summary
The document derives how a Basel-style regulatory risk weight changes when a conservative probability of default is adjusted through Margin of Conservatism Category C. Its central point is that the conservative PD affects the risk weight directly and also changes the regulatory asset-correlation parameter, so the total derivative applies the chain rule through both paths. It develops expressions for the PD adjustment, the PD dependence of correlation, and the partial derivatives of risk weight with respect to PD and correlation.
The author reports numerical agreement between the analytic PD derivative and a finite-difference calculation across a stated PD range, and asks whether the derivation and grade aggregation are correct. That check supports the calculation presented but is not independent validation of regulatory interpretation or aggregation. The formulas depend on the specified risk-weight function, parameter definitions, and assumptions about how MoC changes conservative PD; implementation should confirm those conventions and the applicable CRR treatment.
Key ideas
- A MoC C adjustment changes risk weight through both conservative PD and PD-dependent asset correlation.
- The total sensitivity combines direct and indirect effects using the chain rule.
- The conservative PD derivative follows from the stated scaling relation between best-estimate and conservative PD.
- The document checks its analytic PD derivative against finite differences over a stated PD range.
- Regulatory interpretation and grade-level aggregation are raised as issues but are not independently confirmed.
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# QuantLib in industry # QuantLib in industry How much is QuantLib used in industry and how much street cred does it have? ## Answer by Dirk Eddelbuettel (score 14, accepted) https://quant.stackexchange.com/a/281 It's a very good and useful question. And it is bloody hard to answer just like many other questions relating to the proprietary nature of how banks and funds implement their core technology. A better route may be to ask on the QL lists, and/or to inquire as to who actually attented the first Quantlib forum in London last month. Another route would be to see who StatPro lists as clients. I have been near QL for a long time based on my RQuantLib bindings to GNU R. That obviously covers only a subset of users (those who like R) as well as functionality but I can assure you that I have been in contact with a number of places about it. Which makes perfect sense: this is open source code, so you can always bring it in to at least provide a benchmark or reference implementation. ## Answer by quant_dev (score 16) https://quant.stackexchange.com/a/258 Based on anecdata (conversations with other quants), not much. Banks develop their own models and if they do outsource the effort, they pay someone for the code + support (there are companies like Numerix or Pricing Partners which do that). QuantLib is criticized for being poorly documented and convoluted. My own observation is that the parts of QuantLib I was interested in (LMM) weren't particularly advanced, so if I were to make a call, I would see no point to make an effort to integrate this code with the rest of my bank's systems. ## Answer by David Sokol (score 1) https://quant.stackexchange.com/a/278 I've never heard of it, but I've only been in the industry 2.5 years. Our C++ guys haven't even mentioned it either. They prefer using PACK/LAPACK which is mostly rooted in academia & heavily debugged. We also make heavy use of the IMSL FORTRAN libraries for hardcore statistical computation and Extreme Optimization (for .NET). One of our other researches has reported some interest in the Intel Math Kernel library, but that faded once they saw the price tag. To echo what @quant_dev said, we much prefer to build our own models. ## Answer by fabien (score 1) https://quant.stackexchange.com/a/1100 Same feedback as quant_dev. A few quants are related to Premia but again, not directly used in production. That's more a research consortium and the latest version is not disclosed publicly (but you can pay for it if you want)
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