No-arbitrage options

What this no-arbitrage option pricing question tests

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.

• Replicating portfolios and synthetic construction
• Risk-neutral measure vs. real-world probability
• One-period binomial model
• No-arbitrage as a pricing principle