Put-Call Parity Explained

By Leida Casadiegos · Updated July 2026 · 3 min read · Risk disclaimer

Put-call parity is the fundamental relationship that ties together the prices of a call, a put, the underlying stock and the strike. It sounds academic, but it underpins how options are priced and explains why a call and a put at the same strike are deeply connected.

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The relationship

For European options on a non-dividend stock, put-call parity says: call price + present value of the strike = put price + stock price. In short, owning a call plus cash equals owning a put plus the stock — the two combinations have the same payoff at expiration.

Because the payoffs are identical, the prices must line up. If they did not, a trader could buy the cheaper side and sell the richer one for a risk-free profit, and that arbitrage pressure forces the relationship to hold in liquid markets.

Why it holds

Imagine two portfolios. One holds a call and enough cash to buy the stock at the strike; the other holds a put and one share. Whatever the stock does, both portfolios are worth the same at expiration — so they must cost the same today.

Dividends and interest rates adjust the formula slightly, since holding the stock earns dividends and holding cash earns interest. But the core idea — that calls, puts, stock and strike are locked together — does not change.

What it tells you

Parity explains synthetic positions: a call can be recreated from a put plus stock, and vice versa. Traders use this to hedge, to convert one exposure into another, or to spot when an option looks mispriced relative to its partner.

You do not need to compute parity on every trade, but understanding it demystifies option pricing. It is why implied volatility is consistent between a call and a put at the same strike, and why the two never drift apart for long.

Worked example. A stock trades at $100, the $100-strike call costs $5, and one-month interest is negligible. Put-call parity implies the $100-strike put should cost about $5 as well, since call + strike-cash and put + stock have the same expiration payoff. If the put traded at $4, an arbitrageur could lock in a near-risk-free profit until the prices realign.

Key takeaways

Put-call parity: call + present value of strike = put + stock (European, no dividends).
It holds because a call-plus-cash and a put-plus-stock have identical payoffs.
Arbitrage forces the relationship, keeping calls and puts at a strike in line.
It explains synthetic positions and consistent implied volatility across a strike.

Frequently asked questions

What is put-call parity in simple terms?

It is the rule that a call plus cash equal to the strike has the same value as a put plus the stock, for European options on a non-dividend stock. Because their payoffs match, their prices must line up, which links calls and puts at the same strike.

Why does put-call parity hold?

If the two equivalent combinations had different prices, a trader could buy the cheaper one and sell the richer one for a risk-free profit. That arbitrage pressure keeps the relationship intact in liquid markets.

Does it work with dividends?

The basic formula assumes no dividends and applies to European options. Dividends and interest rates shift it slightly, because holding the stock earns dividends and holding cash earns interest, but the underlying link between calls, puts, stock and strike still holds.

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