Put-Call Parity Calculator

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.

Use the Put-Call Parity Calculator

Put-Call Parity Inputs

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

Put-call parity is a no-arbitrage constraint that links European call prices, put prices, the underlying stock price, and the present value of the strike. Given any three of the four variables — call price (C), put price (P), stock price (S), and strike price (K) — this calculator solves for the fourth. It also shows the parity deviation and the gross arbitrage profit available if the relationship is violated in the market.

How it works

  1. Select a variable to solve, or choose Check Parity / Arbitrage to enter all four market values.
  2. Enter values for the other three variables plus the risk-free rate and time to expiry.
  3. The calculator applies C - P = S - K·e^(-rT) to derive the missing leg.
  4. The parity check section shows the current deviation between the left and right sides.
  5. 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.
  • Check four observed market values directly for a parity deviation.
  • 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: 2026-06-18 · Reviewed by Nham Vu