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.