Put-Call Parity Calculator
Put-call parity is a fundamental no-arbitrage relationship in options theory, applicable to European-style options. It states that the difference between the prices of a call and a put with the same strike and expiration must equal the current stock price minus the present value of the strike price. If this relationship is violated, a riskless profit (arbitrage) is theoretically available. This calculator takes both the actual market prices of a call and a put, plus the underlying stock price, strike price, risk-free rate, and time to expiration, and checks whether the parity holds. It also computes the implied fair put price from the call price (or vice versa) and the parity deviation.
Put-call parity formula
C - P = S - K * e^(-rT)
Fair Put = C - S + K * e^(-rT)
Fair Call = P + S - K * e^(-rT)
Parity Deviation = (C - P) - (S - K*e^(-rT))
Where C is the call price, P is the put price, S is the stock price, K is the strike price, r is the continuous risk-free rate (decimal), and T is time to expiration in years. A deviation of zero means perfect parity; non-zero indicates mispricing.
Parity and synthetic positions
- Synthetic long stock: long call + short put + invest K*e^(-rT) in T-bills.
- Synthetic long call: long stock + long put - invest K*e^(-rT).
- Synthetic long put: short stock + long call + invest K*e^(-rT).
- Parity violations are exploited by arbitrageurs, which quickly restores equilibrium in liquid markets.
- Dividend-paying stocks require adding -PV(dividends) to the right side.
Frequently asked questions
What is put-call parity?
Put-call parity is a no-arbitrage relationship stating that for European options with the same underlying, strike, and expiration: Call - Put = S - K*e^(-rT), where S is the stock price, K is the strike, r is the risk-free rate, and T is time to expiration in years.
What does a parity violation mean?
If the actual call price minus put price differs materially from S - K*e^(-rT), there is a theoretical arbitrage opportunity: buy the cheap side and sell the expensive side. In practice, transaction costs, bid-ask spreads, and short-selling constraints prevent most parity violations from being exploitable.
Does put-call parity apply to American options?
No. Put-call parity holds exactly only for European options. American options can be exercised early, which breaks the exact relationship. For American options, modified inequalities apply: S - K less than or equal to C - P less than or equal to S - K*e^(-rT).
What is the synthetic stock from put-call parity?
Rearranging: S = C - P + K*e^(-rT). This means owning a call, selling a put, and investing the present value of the strike in risk-free bonds is equivalent to owning the stock. This synthetic position is called a synthetic long stock.
How does dividends affect put-call parity?
If the stock pays dividends with present value PV(D) during the option's life, the adjusted parity becomes C - P = S - PV(D) - K*e^(-rT). Dividends reduce the call price and increase the put price relative to a non-dividend stock.
Official sources
- Merton, R. (1973). "Theory of Rational Option Pricing." Bell Journal of Economics 4(1): jstor.org/stable/3003143.
- CBOE Options Institute: cboe.com/education.
- SEC Investor Education: sec.gov/investor.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.