Credit default ($\tau$)

Failure to meet a financial obligation, modeled by a random default time. A zero-recovery default model sets the affected asset value to zero after this time.

Loss given default is the loss conditional on a default, measured as an amount or as a fraction of exposure under the chosen convention. In an independent marked default model the loss amounts are independent marks attached to the events of a Poisson process. Their raw second moment, not just their variance, controls the aggregate compound Poisson distribution variance.

The random time at which credit default occurs. In an observed default model it is a stopping time for the market filtration.

In a deterministic-intensity model, $\lambda (t)$ is the instantaneous conditional default rate given survival and $G(t)$ is the survival probability. Risk-neutral intensity is calibrated for pricing and can differ from the physical intensity used for forecasting losses. More general stochastic-intensity models condition on the underlying filtration and require joint expectations with discounting and recovery.