Probability of Default
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 to recoveries.
Latent Variables
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.
Bernoulli Model - Logistic Regression
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.
The way this is typically done is to use a Logistic Regression to estimate the pd.
Poisson Model
Poisson Model : A poisson distribution is a distibution over a set of counts. That is, it is a discrete prob distibution over the natural numbers (0,1,2...)
where the poisson variable measures a set of counts that occur over a period of time. For instance, if you wanted to predict the number
of phone calls received at a call center over a 10 minute interval, you would use the poisson distribution.
When used in the context of default, the model does not directly model the probability of default, rather, it models the number
of defaults that occur in a given time interval. This is useful in situations where you have a portfolio of loans.
Transition Matrix
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 accomodate credit losses from
write downs.
