# Estimating credit card default probabilities

Folks, I am working on a credit card defaults and transition probabilities. For example a single credit card account could be in a number of states: up-to-date, 30, 60, 90 days in arrears or in default.

• Are there packages in R that do estimation of the transition probabilities given historical monthly cohort defaults?
• Any pointers to papers specific to this type of estimation?
• Simulation of future "paths" of defaults.

Note that transitions occur discretely on a monthly basis.

Thanks much for your time, KW

-
Are you only interested in packages for this in R? (Because if so, this question is off-topic for CV; you may want to read our FAQ.) Or are you also interested in issues related to predicting probabilities in general? Do you have archival data on cases where there is valid info on your predictors & whether or not they ended up defaulting? Are you mostly interested in the probability of defaulting yes or no (a logistic reg type problem), or the time until default (a survival analysis type problem)? –  gung Oct 25 '12 at 21:04
I am not only interested in R packages. I am also interested in papers and/or books that might give guidance and/or examples.As I mentioned in my original note there are multiple transition states. I have monthly data for transitions on thousands of accounts.I need to be able to create a model and then simulate future paths of credit-card collateral. –  kw1958 Oct 25 '12 at 23:34
so you are looking for an HMM? –  Bitwise Oct 25 '12 at 23:49
Are you particularly interested in discrete states (i.e. multiples of 30s)? It could be more natural modeling continuous default rates e.g. as a Gamma. –  Sameer Oct 26 '12 at 4:41
add comment

## 2 Answers

Look at the msm package for R. It will estimate transition probabilities between different states and you can specify which states it is possible to transition between. There are probably other tools as well, msm might be overkill for what you are doing (depending on your questions and the level of detail in your data).

-
add comment

These are "phase type distributions" and great fun! David Lando goes into a lot of detail in "Credit Risk Modeling: Theory and Applications"Credit Risk Modelling: Theory and Applications. Lando details how to model these based on the individual transactions rather than the more crude counts at the end of a month. I'm afraid I don't have my copy here.

How you implement will depend a lot on your exact rules for transitions. What happens for partial payments?

-
add comment