Multi Factor Credit Risk Models

I am working in the area of building credit risk models. Upto this point, the model I have been focused on using the Asymptotic Single Factor Model, more popularly known as Vasicek Single Factor Model. The single factor being representative of the state of the economy.

Now I want to evaluate a more elaborate multiple factor model as used in KMV etc. I am looking specifically for guidance on the following

1. Are their any fundamental papers/references on multi factor credit risk models (A very popular one seems to be one by Michael Pykhtin available here And also one by algorithmics available here.)

2. What should the multiple factors be - geographical location/industry/sector etc.?

3. What would be the expected benefit of multiple factors over a single factor model? Would the Expected Loss, Unexpected Loss and ECAP be expected to be lower/higher compared to a single factor model?

Looking for academicians, industry practitioners, modeling experts for any guidance. Thanks in advance

• Not sure if I missed it, but you never mentioned what asset you're interested in. Credit risk for a car, a house, a mall, a corporation, a country, etc. are very different animals. Oct 15, 2012 at 17:03
• Jeff, somehow missed that in my original post. I am having a portfolio of consumer loans for which the risk characteristics such as PD/LGD/EAD etc. are known. The credit risk model that I am building is to generate the the loss distribution for such a portfolio. It is in this context that I am evaluating multi factor models.
– NaN
Oct 15, 2012 at 19:16
• All, thank you for the help. I want to add another two good references on this area: Paper1 and Paper2. The second paper (Gordy and Heitfield) is one of the very standard references in this area
– NaN
Oct 9, 2013 at 5:56

4 Answers

Most of the credit risk models are some derivative of survival models. Cox Proportional Hazard is one of the early and more popular models, Kaplan-Meier and Logrank tests are others you may have heard of. There are a few ways to go from here. The simplest is to model the sample as binomial with one population as current and the other as in default. A more complex method would be along the lines of an actuarial approach that takes levels of ability to pay into account. A good analogy is levels of sickness to predict potential insurance payouts.

As for what factors used to model, I can't make any suggestions unless I know exactly what asset it is your modeling and what kind of data you have access to - consumer loans is a rather broad description. I'm assuming you're dealing with some type of ABS. If so, then ultimately all you care about is ability to make coupon payments. Credit scores, MSA employment, HPI, LTV, etc. could be of interest - but without more info I can't help much past that.

The goal of a multiple factor model is similar to a single factor, you're just trying to build more confidence in your prediction by explaining more of the variance. Strive for parsimony and don't blindly build on correlations.

• +1 for "don't blindly build on correlations" Oct 17, 2012 at 14:19

For corporate credit portfolios, sector, rating, and maturity are the usual suspects that go into the credit portion of risk model structure, which usually also have interest rates and liquidity pieces.

This book is slightly outdated but will give you a good general introduction.

This presentation may be of interest to you...

https://support.precisionlender.com/entries/22591983-How-does-the-math-work-

Full disclosure: this is my employer, but I think it's relevant to the discussion

• Can you summarize the contents of that presentation in the body of your answer? May 5, 2013 at 0:06

I suggest you to take a look to the CCruncher project, an open-source project for credit risk modeling. It is a framework consisting of two elements: a technical document (introducing the t-Student multi-factor copula model, parameters estimation, etc.), and a software program that implements the Monte Carlo procedure.

Currently, CCruncher considers that factors are industry sectors. It allows the risk disaggregation by region, location, types of obligors, etc.

The discussion 'single factor vs multi-factor' can be responded in the parameter calibration stage and depends on the available historical data and AIC/BIC/DIC values.