Overview
The Td, Lgd, Ead model is a variant of the pd, lgd, ead model. where the probability of default is given by a time to default model.
Time to default is a measure of how old a loan is at the time of default. That is, time of default is a random variable that specifies how much time has elapsed since the loan initiation when the loan defaults. It is usually denoted by {% \tau %}. By definition, the following holds
- {% \tau > 0 %}
- {% \tau %} is either less than or equal to the maturity of the loan, or it is specified to be \infty
PD from TD
Given a time to default model, where {% \tau(t) %} is a probability density function specifying the likelihood that the time of default is {% t %}, the probability of default within the time interval {% a \leq \tau \leq b %} is given by
{% \displaystyle PD = \int_a^b \tau(t) dt %}
Time of Default as a Poisson Model
The typical way to model time to default is as a Poisson distributed variable. (see Poisson Default Model for more information)