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Binary Call Pricing via Differentiation (Part 2) is a hard quant interview question on option theory.
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This is a hard option-theory problem that tests whether you can connect the discrete payoff structure of a digital option to the continuous framework of vanilla European calls. It requires fluency in risk-neutral valuation, replication arguments, and calculus-based reasoning about limits.
The question probes your ability to set up a replicating portfolio in continuous time and then take a mathematical limit to uncover a deep relationship between option prices. Specifically, you'll need to recognize how the payoff of a binary call can be expressed in terms of the derivative of vanilla call prices with respect to the strike, and justify this connection via arbitrage-free pricing principles. Traders and quant researchers rely on this kind of reasoning to hedge exotic payoffs using liquid vanilla instruments.