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European Put–Call Parity & Discounted Strike

Relate European call and put prices for the same non-dividend-paying asset, strike and expiry using annual discounting.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

For a spot price of 100, a put worth 5 and a strike of 110 due in one year at a 10 percent annual rate, discounted strike is 100 and parity gives a call worth 5.

Call + K/(1 + r)^T = spot + put

Worked example

Enter these known values and leave the other values blank.

Underlying spot price
100 USD
European put premium
5 USD
Common strike at expiry
110 USD
Years until common expiry
1 year(s)
Annual effective discount rate
10 %
European call premium
5 USD
Present value of the strike
100 USD

Assumptions and limitations

  • The call and put are European, with identical underlying, strike and expiry. The underlying pays no dividends or other distributions before expiry.
  • Discounting uses an annual effective rate and a positive remaining term. The annual rate must exceed minus 100 percent; this is not continuous discounting.
  • Premiums, spot and strike use matching per-unit or matching contract amounts. Do not mix a per-share price with a whole-contract premium.
  • The identity assumes frictionless no-arbitrage financing. Negative premiums, a call above spot or a put above discounted strike are inconsistent with this model. An inverse term at a zero rate can be undetermined.

Common questions

Does this directly apply to American options?

No. Early exercise changes the conditions. This equation is for European options with matching contract terms.

Can I use it for a dividend-paying stock?

This version omits dividends. A dividend-paying underlying needs the appropriate distribution adjustment.

References

Bookify requires nonnegative option and strike values, positive annual discount factors, and the elementary call and put upper bounds for this model.

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