Marginal and Conditional Default Probabilities and Hazard Rates

Summary

The document raises a conceptual question about forward default probability, conditional default probability, marginal default probability, and hazard rate. It asks whether the probability of default over a future interval should be expressed as the probability of surviving to that interval multiplied by the forward probability of default conditional on survival.

This distinction matters in credit-risk analysis because an unconditional probability of default over a period and a conditional probability given survival to its start are different quantities. The former incorporates the chance of reaching the period alive; the latter describes default risk within that period for an issuer that has survived so far. A hazard rate is a rate-like measure of instantaneous conditional default risk, rather than simply either probability without specifying a time interval. The document contains no diagram or answer, so it does not establish whether a particular calculation is correct or provide conventions for discrete versus continuous time.

Key ideas

• A forward default probability can be conditional on survival to the beginning of its interval.
• An unconditional marginal default probability includes the probability of surviving to the interval first.
• The unconditional probability over an interval can be formed from survival probability multiplied by conditional forward default probability.
• A hazard rate describes instantaneous conditional default risk and is not interchangeable with an interval probability.

Tags

# Normal default probability vs forward default probability/conditional default


# Normal default probability vs forward default probability/conditional default












is the diagram correct in calculating foward PD(conditional default) ? Or should the formula be

Probability of default = probability of survival x forward PD

Which of this is equal to marginal PD(unconditional) and which of this is equal to hazard rate?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.