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A binary option (also known as all-or-nothing option) is a financial contract that entitles its holder to a fixed payoff when the event triggering the payoff occurs or zero payoff when no such event occurs.

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A binary call option is, at long expirations, similar to a tight call spread using two vanilla options. One can model the value of a binary cash-or-nothing option, C, at strike K, as an infinitessimally tight spread, where is a vanilla European call:

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