= Barrier-triggered put
{title2=$\tau=\inf\{u\geq t:S_u\leq B\}\wedge T$}
= Exploding put
{synonym}
A put with a prescribed exercise rule: exercise at the first touch of $B<K$, or at expiry if no touch occurs. Its value is bounded above by the <American put option>, which optimizes over exercise times. With zero interest rate, its value equals the <down-and-out put> value plus $(K-B)$ times a cash-at-expiry <one-touch option> value. At positive interest rate the rebate is paid at touch, so replacing it by an expiry payment would generally be incorrect.
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