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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.

A stock model whose price can be killed or reduced at a default time. The zero-recovery default model combines continuous price dynamics before default with a jump to zero.

For an independent exponential distribution default time of rate $\lambda$ and a continuous nonnegative martingale $S$, this process is a martingale. The compensating pre-default factor $e^{\lambda t}$ balances the survival probability $e^{-\lambda t}$. The strict survival inequality gives a càdlàg price process.