Put-Call Parity in a Flash

This question focuses on the foundational no-arbitrage relationship linking European calls, European puts, the underlying stock, and a risk-free bond in a simple market without dividends. The candidate is asked to recall the standard put-call parity identity and then justify why it must hold in an arbitrage-free setting. The context is clean and stylized: same strike, same maturity, and no cash flows in between, making it a classic entry-level options pricing question often seen in interviews for trading, structuring, and derivatives research roles.

Answering it well draws on comfort with payoff diagrams, constructing equivalent portfolios, and reasoning about cash flows at maturity versus today. The proof typically hinges on building two portfolios with identical terminal payoffs and arguing that their current values must coincide under no-arbitrage. Interviewers watch for precise definitions, correct use of the risk-free discount factor, and a logically tight argument rather than memorized formulas. They also look for awareness of the assumptions behind the relationship and the ability to discuss how relaxing them (for example, introducing dividends) would alter the pricing identity.

What it tests

The core structure underlying put-call parity is the equivalence of payoffs between different portfolios constructed from basic financial instruments, enforced by the no-arbitrage principle. If two portfolios guarantee the same payoff in every possible future state and require no interim cash flows, then their present values must be equal; otherwise, arbitrage opportunities would exist. This is not unique to options: it is a general property of financial markets where replication is possible. The principle holds because, in efficient markets, any divergence in value between perfectly replicating portfolios would be immediately exploited by traders, driving prices back into alignment. Thus, the relationship between option prices, the underlying asset, and the risk-free bond is governed by the requirement that no combination of these can yield a riskless profit without investment.