# Name for option valued by a time difference

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.

• Is $T_1$ a stochastic time before $T_0$, or does the payoff depend on the stock going below $Y$ at any date up until $T_1$, with $T_1$ a fixed date? Sep 20 at 9:27
• @Kermittfrog I should have been clearer about the parameters. The contract specifies $X$, $Y$, $T_0$ and $c$. If such a $T_1$ occurs, then there's a payout. This is the latter formulation you suggest. Sep 20 at 15:55
• Did you see such an option? Never heard of it, but would like to know what problem this would solve (what purpose the product has). Sep 22 at 19:39