Binary Option Delta at Expiry - Quant Trader Interview Question
Difficulty: Hard
Category: Options & Greeks
Practice quant interview questions from top firms including Jane Street, Citadel, Two Sigma, DE Shaw, and other leading quantitative finance companies.
Topics: options, delta, binary-option, greeks, dirac-delta
Problem Description
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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