What is put-call parity?

Put-call parity is a no-arbitrage identity for European options: C - P = S - K·e^(-rT). It states that the difference between the call and put price must equal the stock price minus the present value of the strike. Any deviation creates a riskless profit opportunity.

Does put-call parity apply to American options?

No. American options allow early exercise, which breaks the strict equality. For American options a weaker inequality holds: S - K ≤ C - P ≤ S - K·e^(-rT). This calculator applies only to European-style options.

What does the arbitrage profit represent?

It is the gross profit per share (before transaction costs and margin requirements) from a self-financing portfolio that exploits the parity deviation. Divide by the contract multiplier (usually 100) for the per-contract dollar amount.

How is the discount factor e^(-rT) calculated?

The formula uses continuous compounding: PV(K) = K × e^(-rT), where r is the annualized risk-free rate as a decimal and T is time to expiry in years. For 6 months at 5%, PV = K × e^(-0.05×0.5).

What are typical inputs for the risk-free rate?

Use the prevailing short-term government rate for the option's currency — for USD options, the 3-month T-bill rate or SOFR is common. Enter as a percentage (e.g. 5 for 5%).

Put-Call Parity Calculator

Name: Put-Call Parity Calculator
Availability: InStock
Author: Nham Vu

Verify or solve the put-call parity relationship C - P = S - K·e^(-rT) for European options. Solve for any missing leg and quantify any arbitrage profit when parity is violated.

Put-Call Parity Inputs

Solve for

Call Price C ($)

Put Price P ($)

Stock Price S ($)

Strike Price K ($)

Risk-Free Rate r (%/yr)

Time to Expiry T (years)

Put-Call Parity Identity

C − P = S − K · e^−rT

C = European call price

P = European put price

S = Current stock price

K = Strike price

r = Risk-free rate (annual)

T = Time to expiry (years)

Summary

Verify or solve the put-call parity relationship C - P = S - K·e^(-rT) for European options. Solve for any missing leg and quantify any arbitrage profit when parity is violated.

How it works

Select which variable you want to solve for: call price, put price, stock price, or strike price.
Enter values for the other three variables plus the risk-free rate and time to expiry.
The calculator applies C - P = S - K·e^(-rT) to derive the missing leg.
The parity check section shows the current deviation between the left and right sides.
If a deviation exists, the arbitrage section shows the gross profit per contract available by exploiting it.

Use cases

Verify that live option quotes satisfy put-call parity before placing a spread trade.
Back out an implied stock price from call and put quotes when the underlying is illiquid.
Derive a fair put price from a known call price to check for mispricing.
Estimate the implied risk-free rate embedded in option market prices.
Detect arbitrage opportunities when call and put premiums diverge from parity.
Study the parity relationship in CFA, FRM, or derivatives coursework.

Frequently Asked Questions

Last updated: 2026-07-23 · Reviewed by Nham Vu