# credit risk - How to calculate the probability of default (private companies)?

Part of my master thesis I am working with a company. I have the project to use their financial database with all the financials data (7 years) of approximately 3’000 companies.

They have their own credit score from 1 that is the best score, to 4 the worst. What I intend to do is to calculate the Z-score (Altman score) and do a corresponding map between these two scores.

My ultimate goal is to compute the probability of default for these two different credit score.

Could you advise me if my logic of how to do it is correct? Or I am free to take any advises with a different approach. For instance I am hesitating to use the Black-Schole-Merton model to have the probability of default.

My first step is: calculate the Z-score of each company with this formula:

Formula for Private Companies: (Altman 2000) : Z' = 0.717*X1 + 0.847*X2 + 3.107*X3+ 0.420*X4+0.998*X5

X1=Working Capital/Total Asset

X2=Retained Earnings / Total Assets

X3=Earnings Before Interest and Taxes / Tot Assets

X4=Book Value of Equity / Book Value of Total Debt

X5=Sales / Total Assets

2nd step: I would like to do a corresponding table between the internal credit score and the Z-score.

3rd: create a normal distribution to find the probability of default. BUT on this part I would need some advise to see how it is possible.

I hope I am clear in what I would like to do. Thank you in advance.

• Why don't you wanna use Merton model? – Egodym Sep 8 '15 at 20:44
• @Egodym , I would use it as a second indicators. But the reason why I want to use Z score is that the company knows it and use it sometimes for their risk score. – manu Sep 9 '15 at 2:15
• Most of the time logistic regression is used to estimate PD – adam Feb 25 '16 at 10:21
• Hi How did you solve this issue ? Even I am facing this issue , I have credit scores but need to find a probability of default – user19904 Mar 15 '16 at 12:16
• The Z score does not easily translate into probability of default. For that and a few other reasons, RiskMetrics (which uses the Merton Model)consulted with Altman and produced something called Z-Metrics. You might want to read a representative paper at federalreserve.gov/newsevents/rr-commpublic/… . Click on it and search for the term Z-Metrics or Z-score starting around page 469. Of course you can always come up with some way to map the Altman scores to something but I just thought you might be interested to see other possibilities. – horseless Mar 15 '16 at 18:33