⚖️ Put‑Call Parity Calculator
Verify the no‑arbitrage relationship and derive the implied price for the missing leg.
LHS: C + K·e^(-rT)
105.1229
RHS: P + S
110.0000
Difference (LHS − RHS)
-4.8771
Implied Put from parity
5.1229
Implied Call from parity: 14.8771
How to Use This Calculator
Put‑call parity links the prices of European calls and puts with the same strike and expiry via the relationship C + K·e^(-rT) = P + S. Provide spot S, strike K, the annual continuously‑compounded risk‑free rate r, time to expiry T in years, and any two of C or P. The tool checks parity by comparing the left and right sides and derives the implied price for the missing leg. Small deviations can occur due to discretization, funding frictions, or dividends. For assets with dividends, use the forward‑adjusted form or Black–Scholes with dividend yield for more precise valuation.
Formula
C + K·e^(-rT) = P + S
Implied Put: P = C + K·e^(-rT) − S, Implied Call: C = P + S − K·e^(-rT)
About Put‑Call Parity Calculator
Put‑call parity is a fundamental no‑arbitrage relationship in option pricing. It ensures that a synthetic forward created by buying a call and selling a put equals the present value of entering a forward contract on the same underlying. Persistent deviations from parity would allow arbitrage by constructing replicating portfolios. In practice, observed differences are usually explained by discrete dividends, differing carry costs, borrowing constraints, or bid‑ask spreads. Use this tool to validate quotes, infer a reasonable value for a missing leg, or teach the intuition behind option replication without diving into more complex models.
Frequently Asked Questions
Does parity hold for American options?
Strict equality holds for European options. For American options, early exercise can introduce inequalities rather than equalities. The relationship becomes a bound rather than an exact equation, particularly for puts that may be exercised early when rates are high.
How do dividends affect parity?
For known discrete dividends, subtract the present value of dividends from S, or use a continuous dividend yield adjustment S·e^(-qT). The parity becomes C + K·e^(-rT) = P + S·e^(-qT) + PV(dividends), depending on the convention used.