Probability of default, cumulative, marginal, hazard rate

[Jeffrey Chudy]

Probability of default, cumulative, marginal, hazard rate

[Anonymous]

Hi Mukul,

Do you have a this material in a tutorial? I.e. how to convert to and from Probability of default, cumulative, marginal, hazard rate given a couple pieces of information?

Thanks!

[Anonymous]

No, not yet. But maybe that is a good topic to write on. Briefly, the marginal probability of default is the probability the bond will default in a given year, conditional on it having survived till the end of the previous year. The marginal probability of default in year 5 means the bond defaults in year 5 alone, and has survived till the end of year 4.

The cumulative probability of default is the probability that the bond would have defaulted in any of the years including the particular year in question, eg, the cumulative probability of default in year 5 means the probability that the bond would have defaulted in either year 1, 2, 3, 4 or 5.

The hazard rate is the probability of default effectively converted to a continuously compounded rate, that is the easiest way to understand that. (The ‘hazard rate’ makes calculations a bit simpler, and helps tie probability of defaults to CDS pricing.)

There is a tutorial on default correlations though – http://www.riskprep.com/all-tutorials/37-exam-3/114-default-correlations

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