Is there a name for an option whose value is determined by a time difference?
I mean a derivative whose contract reads something like, "If stock $X$ goes below $Y$ at time $T_1$, and $T_1$ is before $T_0$, pay out $c\times(T_0-T_1)$".
The exposure is similar to that of an annuity, but different enough that I wondered whether it had a name of its own.