# Generalized Linear Mixed Model (GLMM) for the probability of default of corporates

I work in the financial industry and we want to implement an internal rating model for our clients (think corporates large or mid , banks etc. some listed on an exchange some others not).

We want to give ratings (A,B,C etc.) according the probability of default each client will be assigned -say pd's of $$0-0.05$$ goes to credit category A $$0.06-0.1$$ to category B and so on.-

I have studied the literature quite well and my background is qfin and maths.

I ended up thinking that a simple logistic regression is quite good but adding random effects would be interesting since they can capture dependence structures among defaults (i.e. in the firms in the same sector). My data will be financial ratios for each firm for a period of time (say 5-10 years) and if defaulted (1) or not (0) I though of having the financial ratios as fixed effects and the sector and the year as random. Do you think this approach makes sense?

PS i am using R.

Merton models and their progeny are likely the route you want to take. There's a ton of research out there on this, model selection largely depends on the use for your product (eg, loan or firm risk management, trading, etc).

Regression here is likely insufficient given the amount of very public research on the topic. Regulators care a great deal about this topic, so your real answer to this should be in context of discussion with regulator-facing business partners and your model validation team. Unless, of course, this is a type of side project that has limited business implication.

• Maybe i am not that familiar with the Merton Model and all the derivatives of it, but in the case of private companies (i.e. not listed on an Exchange) I don't see how it could work... Further I work for a CCP and for example the Austrian CCP has the following approach ccpa.at/en/risk-management/credit-assessment which is presumably more in my line of thought. – Stelios Kounis Apr 9 at 10:11
• You don't need trading data to make use of a Merton model. Banks regularly use them for loan books. Again, regression seems elementary here and may face regulator scrutiny. What will your model be used for? – Kch Apr 9 at 20:34
• An internal credit rating model is required for Central Counterparties (CCP's) that operate in the European Union and want to be EMIR compliant (just some EU regulations). I do not think that a regulator would have any problem with such a model, i do not see the reason why he should... Fact is that many EU CCP's seem to use some type of regression for the credit scores, one more example is this nasdaq.com/docs/Credit-Score-Guideline.pdf – Stelios Kounis Apr 12 at 7:39