Put-Call Parity

Options
Updated Apr 2026 • Has calculator

The no-arbitrage relationship between European call and put prices on the same underlying.

What is Put-Call Parity?

Put-call parity states that for European options with the same underlying, strike, and expiry, the difference between the call and put price must equal the spot price minus the present value of the strike: C − P = S − K·e^(−rT). Any deviation from this relationship creates a risk-free arbitrage opportunity. This calculator shows the discrepancy between observed prices and the parity condition.

Formula

C − P = S − K·e^(−rT)

Worked Example

Worked example — Illustrative example (S=100, K=100, r=5%, T=1 yr)

Textbook example — Hull (2021)

Step 1  Call price (C): $10.45, Put price (P): $5.57
Step 2  Stock price (S): $100, Strike (K): $100
Step 3  Risk-free rate: 5%, Time to expiry: 1 year
Step 4  LHS: C − P = 10.45 − 5.57 = $4.88
Step 5  RHS: S − K·e^(−rT) = 100 − 100×e^(−0.05) = 100 − 95.12 = $4.88
Step 6  Discrepancy: $0.00 — parity holds exactly
Step 7  → A non-zero discrepancy signals a potential arbitrage opportunity

Source: Hull, J.C. — Options, Futures, and Other Derivatives, 11th ed., Ch. 11 (2021-01-01)

Calculate Put-Call Parity

Observed market price of the call option

Observed market price of the put option

Current market price of the underlying stock

Common strike price of both options

Annual risk-free rate

Time to expiration in years

Parity Discrepancy

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Not investment advice.

How to Interpret Put-Call Parity

< -0.1
Put overpriced vs call — potential arbitrage
-0.1 – 0.1
Parity holds — no arbitrage opportunity
> 0.1
Call overpriced vs put — potential arbitrage

📚 Advanced Options — Complete the path

  1. Implied Vol (IV)
  2. Put-Call Parity
  3. Time Value
  4. Rho (Call)
  5. BS Put
Sources
  1. Hull, J.C. — Options, Futures, and Other Derivatives, 11th ed.
  2. Investopedia — Put-Call Parity