Cash-or-nothing options have European-style exercise with payoff $$ \begin{align*} \mathrm{payoff} = \begin{cases} 0 \quad & \mathrm{if} \quad S \leq K\\ P \quad & \mathrm{otherwise} \end{cases} \end{align*} $$ and $$ \begin{align*} \mathrm{payoff} = \begin{cases} 0 \quad & \mathrm{if} \quad S \geq K\\ P \quad & \mathrm{otherwise} \end{cases} \end{align*} $$ for a put, where $K$ is the strike, $P$ is the payment amount and $S$ is the spot.
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