Put-Call Parity Calculator

What the put-call parity calculator does

The put-call parity calculator derives the fair price of a European put option from the price of the matching call. Parity is a no-arbitrage identity, not a forecasting model, so it holds in every market and currency and for any underlying asset, from equities and indices to commodities and foreign exchange.

You supply the call price and a few market inputs, and the tool returns the put price that must hold if the market offers no free lunch. You can use it to fill in a missing quote, check the prices you are shown, and see how calls, puts, and the underlying are linked.

How put-call parity works

Put-call parity links a call, a put, the underlying asset, and a risk-free bond. Two different portfolios can produce exactly the same payoff at expiry, so they must cost the same today; otherwise a trader could buy the cheaper one, sell the dearer one, and lock in a riskless profit.

Holding one call plus enough cash to buy the underlying at the strike on expiry gives the same payoff as holding the underlying plus a put with the same strike. Because the payoffs match in every outcome, the present values must match too. Rearranging that equality gives the formula the calculator uses:

P = C – S + K x e^(-rT)

C is the call price, S the current underlying price, K the strike, r the continuously compounded risk-free rate, and T the time to expiry in years. K x e^(-rT) is the strike discounted back to today.

The inputs

• The call price is the observed market premium of the call, the anchor from which the put price is derived.
• The underlying price is the current price of the asset the options are written on. A higher underlying price, all else equal, lowers the implied put.
• The strike price is the common exercise price of both options. A higher strike raises the put, because the right to sell at a higher level is worth more.
• The risk-free rate discounts the strike. A higher rate reduces the present value of the strike, which reduces the implied put.
• Time to expiry is the number of years until the options expire. More time increases the discounting of the strike.

Reading the results

The implied put price is the premium a European put must trade at for parity to hold. The present value of the strike shows what the exercise price is worth in today's money. The parity residual measures how well the two sides of the equation balance; when the put is derived from the call it is zero by construction, and it becomes useful only when you compare the model price with an independently quoted put.

A persistent, meaningful gap between the parity price and a real market quote points to something the simple formula leaves out, most often dividends, the cost of borrowing the underlying to short it, or American rather than European exercise.

Using parity to spot arbitrage

If the observed call, put, and underlying prices do not line up with the formula, there may be an arbitrage: a combination of trades that produces a guaranteed profit wherever the underlying finishes. In liquid markets these gaps are tiny and vanish quickly, but checking parity helps catch mispriced quotes, stale data, and input errors before they become losing trades.

For investors who never trade options, parity explains why puts and calls move together and why an expensive call implies an expensive put on the same terms. It also shows how to build a synthetic put from a call, a synthetic call from a put, or a synthetic forward from the two options combined.

Assumptions and limitations

Put-call parity is exact only under idealised conditions: European exercise, no dividends before expiry, a single risk-free rate for borrowing and lending, and frictionless trading with no transaction costs or bid-ask spreads. Real markets violate these to some degree, so observed prices sit close to, but rarely exactly on, the parity line.

Treat the result as a benchmark. For a dividend-paying underlying, subtract the present value of expected dividends from the underlying price first. For American options, early-exercise value can push real prices away from strict parity, especially for deep in-the-money puts.

This article is general information only and is not financial advice.

About This Put-Call Parity Calculator

Use this put-call parity calculator to get an instant estimate based on the figures you enter. Adjust the inputs above to match your situation, or browse all our calculators to plan your next step.