Put Call Parity Calculator
Calculate options pricing relationships and identify arbitrage opportunities using put-call parity
Calculate Put-Call Parity
Current market price of the put option
Current market price of the underlying asset
Exercise price of both options
Time until options expire (in years)
Annual risk-free interest rate (e.g., Treasury rate)
Put-Call Parity Results
Example Calculation
Apple Stock Options Example
Spot Price (S): $150.00
Strike Price (X): $155.00
Call Price (C): $8.50
Put Price (P): $12.00
Time to Expiry: 0.25 years (3 months)
Risk-Free Rate: 5%
Calculation
PV(X) = $155 / (1.05)^0.25 = $153.09
Left Side: C + PV(X) = $8.50 + $153.09 = $161.59
Right Side: P + S = $12.00 + $150.00 = $162.00
Difference: $0.41 (Put slightly overpriced)
Parity Components
Call Option
Right to buy asset at strike price
Put Option
Right to sell asset at strike price
Spot Price
Current market price of asset
Present Value
Discounted value of strike price
Trading Tips
Only applies to European options (exercise at expiry only)
Assumes no dividends and no transaction costs
Price discrepancies may indicate arbitrage opportunities
Use current risk-free rate (e.g., Treasury bill rate)
Understanding Put-Call Parity
What is Put-Call Parity?
Put-call parity is a fundamental relationship in options pricing that establishes a theoretical equilibrium between the prices of European call and put options with the same strike price and expiration date, the underlying asset price, and the risk-free rate.
Why is it Important?
- •Identifies arbitrage opportunities in options markets
- •Helps determine fair value of options
- •Provides basis for synthetic instrument creation
- •Ensures consistent options pricing models
The Put-Call Parity Formula
C + PV(X) = P + S
- C: European call option price
- P: European put option price
- S: Current spot price of underlying asset
- PV(X): Present value of strike price
- PV(X) = X / (1 + r)^T
Note: This relationship assumes no dividends, European-style exercise, and frictionless markets with constant risk-free rates.
Arbitrage Strategies
When Call is Overpriced
If C + PV(X) > P + S:
- • Sell the call option
- • Buy the put option
- • Buy the underlying asset
- • Invest PV(X) at risk-free rate
When Put is Overpriced
If P + S > C + PV(X):
- • Buy the call option
- • Sell the put option
- • Short sell the underlying asset
- • Borrow PV(X) at risk-free rate