Overview
Probability of Default is the probability that a given asset goes into a state of default. When analyzing default, one must start with a definition of default. The typical definition of default is 90 days past due on payments, although other time frames are used as well.
For simplification, it is typically assumed that an asset in default is always in default, that is, even if the asset cures (begins making all payments), the payments from the point of default are considered as recoveries.
PD Time Frames
When designing a PD model, it is important to understand the time frame under consideration. That is, a probability of default is a probability that the asset defaults over a specified time frame. For example, the probability of default could be considered as the probablity that the asset defaults over the next month, or year, or possibly an infinite horizon, in which case the probability of default is the probability that the asset will ever default.
When the time frame is taken to be less than the length of the loan, there is an oppurtunity to construct a probability of default for each time period between now and the maturity. For example, one could construct a probability of default over the next month, but then estimate the probability of default for each subsequent month. In such a case, this series of pd models effectively becomes a time to default model.
Pd Models
- Bernoulli Model : The Bernoulli Model is a direct model of the probability of default. That is, it assumes for each loan, there is a probability of default, based on a possible set of factors (loan age, economic factors...), and the bernoulli model seeks to measure that probability of default directly.
- Poisson Model : The Poisson model is a time to default model which can be used to calculate a probability of default
- Transition Matrix : The transition matrix method models the credit quality of a loan in addition to default. It assigns a set of credit ratings to a loan and models the probability that a loan transitions from one rating to another, creating a model that can accommodate credit losses from write downs.
- Latent Variables : the latent variables framework provides a way to model the probability of default, which is particularly useful for calculations, especially when dealing with correlations among defaults.