# KMV-Merton Probabilties of Default vs Moody's EDF

Moody's used to publish probability of default estimates from their Moody's EDF model, but they have temporarily discontinued it. I understand that the Moody's EDF model is closely based on the Merton model, so I coded a Merton model in Excel VBA to infer probability of default from equity prices, face value of debt and the risk-free rate for publicly traded companies.

However, the probabilities of default that I get from the Merton model are drastically different from the Moody's EDF model. Generally they're extremely high or extremely low and the ranking of the same firms is totally different. I understand that Moody's uses an empirical distribution while Merton uses a normal distribution in order to calculate these probabilities - is this the only source of the discrepancy?

If I want to accurately reproduce Moody's EDF probabilities of default, what approach should I use? Since I can't reproduce their empirical distribution, is this pointless?

I'd be happy to post my code if anybody is interested.

• I have to find a source, but if I recall correctly, KVM doesn't use a distribution to find the PD as the Merton model does. It has a set of mappings that it uses. I'll find a source and get back to you – AfterWorkGuinness Oct 1 '15 at 14:56

I understand that Moody's uses an empirical distribution while KMV uses a normal distribution in order to calculate these probabilities

KMV doesn't use a normal distribution to map distance to default to a probability of default (EDF in the KMV model). It uses a proprietary database.

By a strict structural interpretation, $EDF$, the expected default frequency, meaning the probability of observing the firm to default within one year, ought to equal the normal probability $EDF_t=N(DD_t)$. KMV, however, breaks the model at this point, and instead relies on its large database of historical defaults to map $DD$ to $EDF$ by a proprietary function $EDF = f(DD)$.

• Yeah you're right. The Normal distribution is used in the model that I coded in VBA, which is the Merton model for probability of default. Calling it KMV-Merton is inaccurate. – beeba Oct 1 '15 at 15:23

If I want to accurately reproduce Moody's EDF probabilities of default, what approach should I use?

You may find

Sreedhar T. Bharath, Tyler Shumway; Forecasting Default with the Merton Distance to Default Model, The Review of Financial Studies, Volume 21, Issue 3, 1 May 2008, Pages 1339–1369, https://doi.org/10.1093/rfs/hhn044

interesting. They do what you describe to some length. See particularly page 1354. They find a high rank correlation which makes this observation you make odd

... the ranking of the same firms is totally different.

Though, their sample size is only 80. The nominal default probability levels are though rather off which is the reason that they use a Cox model.

... is this the only source of the discrepancy?

As far as I know, then maybe. Other differences you get may be due to what they use as e.g., the debt.