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Put-Call Parity Calculator

Enter the call price, spot, strike, rate and time to expiry to get the implied put price.

How it is calculated

The tool solves put-call parity for the put: P = C − S + K × e−(r/100) × t. C is the European call price, S the current price of the underlying, K the strike, r the annual risk-free rate entered as a percentage (5 means 5%) with continuous compounding, and t the time to expiry in years (0.5 is six months). The term K × e−rt is the strike discounted to today. Prices and strike must be zero or higher, and all five fields must be filled in. The formula assumes European options, the same strike and expiry for both options, and no dividends. The result is in dollars; a negative result means the inputs are inconsistent.

Worked example

A one-year European call with strike 100 trades at $8.50, the stock is at 100, and the risk-free rate is 5%. Step 1: discount the strike, 100 × e−0.05 = 95.1229. Step 2: P = 8.50 − 100 + 95.1229 = 3.6229. The tool shows an implied put price of $3.62. If the market quotes that put at, say, $4.50, parity is broken, which may signal a mispricing or an input that has been left out.

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Common mistakes

  • Typing the rate as 0.05 instead of 5; the tool divides by 100, so 0.05 means 0.05% and the discounting nearly disappears.
  • Entering time in months or days instead of years, which changes the discount factor completely.
  • Applying the result to American options or to stocks that pay dividends before expiry; parity in this form holds for European options without dividends.
  • Using a call and a put with different strikes or expiries, which breaks the identity.
  • Ignoring a negative result: a negative implied put price means the call price entered is too low for the spot and strike given.

Sources

About this calculator

Put-call parity is a no-arbitrage identity linking the prices of a European call and put with the same strike and expiry on the same underlying: C − P = S − K·e^(−rt), where S is the spot price, K the strike, r the risk-free rate, and t the time to expiry. Rearranged, the implied put price is P = C − S + K·e^(−rt).

If the relationship doesn't hold in the market, an arbitrageur can lock in a risk-free profit by simultaneously trading the option, its counterpart, and the underlying — which is why parity holds tightly in liquid options markets. Traders use it to check option prices for mispricing and to construct synthetic positions (e.g., a synthetic long call from a put plus stock).

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