Difficulty: Medium
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: barrier-options, knock-in, knock-out, parity, options
You are a trader at a high-frequency trading firm. You are tasked with understanding the relationship between different types of barrier options. Consider a European call option with a strike price of $K$ and an expiry of $T$. You also have a knock-in call option and a knock-out call option, both with the same strike price $K$, expiry $T$, and barrier level $B$ where $B < K$. All options are on the same underlying asset. Assuming continuous monitoring of the barrier, what is the relationship bet
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