One Step Ahead

What this no-arbitrage option pricing question tests

This is an easy option-theory question that introduces the core principle of risk-neutral pricing in a one-period binomial model. It is the foundational building block for how trading desks and quant funds value derivatives, and it appears regularly in initial screening interviews.

The question asks you to move beyond intuition about probabilities and instead use the no-arbitrage principle to derive a fair price. Rather than guessing what the stock "probably" does, you construct a replicating portfolio (or equivalently, compute the risk-neutral probability) and discount the expected payoff. The zero interest rate simplifies the mechanics without hiding the core logic.

• Binomial model and state-space decomposition
• Replicating portfolios and synthetic hedging
• Risk-neutral measures versus real-world probabilities
• Option payoff at expiration and present value