Defaults instantaneous probability

The hazard rate characterizes the instantaneous probability of default of the credit risky underlying exposure. As each of the components above may not be static over time and a pricing model may... 

As the hazard rate (or instantaneous probability of default) rises then the credit spread increases. 

A hazard rate function may be determined from the term structure of credit. The hazard rate function has its foundation in statistics and may be linked to the instantaneous default probability. 

Oversimplified in the above example, the occurrence of a default is actually a Poisson process, with the occurrence of a default in time interval u governed by hazard function X(u), which defines the instantaneous default rate at any point in time du. The probability of survival to time t, according to the Poisson distribution, is... 

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See also in sourсe #XX -- [ ]

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