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No-arbitrage options is a easy quant interview question on option theory.
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This is an easy option-theory question that introduces the core principle of risk-neutral valuation. Trading desks and quant funds ask variants of this problem to verify that candidates understand how to price derivatives without assuming any real-world probability or requiring a discount rate.
The key insight is that arbitrage-free pricing does not depend on the actual likelihood of stock movements—only on the replicating portfolio (or equivalently, the risk-neutral measure). A structured approach involves identifying the option's payoff in each final state, constructing a hedge, and solving for the unique price that prevents riskless profit.