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Difficulty: Hard
Category: Options & Greeks
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Topics: options, delta, binary-option, greeks, dirac-delta
Consider a cash-or-nothing call option with a strike price of K. This option pays you 1 if the underlying asset price, $S_T$, is greater than K at expiry T, and 0 otherwise. What happens to the delta of this binary option as time to expiry, $t$, approaches 0? Assume the underlying asset price follows a continuous path.
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