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TL;DR

The fundamental relationship between European call and put prices: \( C - P = S - Ke^{-rT} \). Equivalently, a call plus a bond equals a put plus the stock.

By Valenke Exam Prep Team·Last updated 2026-06-03

Put-Call Parity

The fundamental relationship between European call and put prices: \( C - P = S - Ke^{-rT} \). Equivalently, a call plus a bond equals a put plus the stock.

Why it matters for interviews

One of the most testable concepts in quant interviews. It is model-free (holds regardless of the pricing model), enables arbitrage detection, and is used to derive put prices from call prices and vice versa.

Definition and Mathematical Foundation

The fundamental relationship between European call and put prices: \( C - P = S - Ke^{-rT} \). Equivalently, a call plus a bond equals a put plus the stock.

Application in Quantitative Finance

One of the most testable concepts in quant interviews. It is model-free (holds regardless of the pricing model), enables arbitrage detection, and is used to derive put prices from call prices and vice versa.

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Frequently Asked Questions

How do you prove put-call parity?▼
Compare two portfolios at expiration: (1) Long call + \( Ke^{-rT} \) cash, and (2) Long put + stock. Both give \( \max(S_T, K) \) at expiration. By no-arbitrage, they must have the same value today.
Does put-call parity hold for American options?▼
Not as an equality. For American options: \( S - K \leq C - P \leq S - Ke^{-rT} \). Early exercise possibility breaks the exact equality but bounds the relationship.
How is put-call parity used for arbitrage?▼
If \( C - P \neq S - Ke^{-rT} \), construct a riskless arbitrage: buy the underpriced side and sell the overpriced side. Transaction costs and dividends must be accounted for in practice.