Definition
Put-call parity states that the price of a European call minus a put equals the present value difference between the stock price and the strike price. This arbitrage relationship ensures that calls and puts are consistently priced. Violations create riskless profit opportunities. The relationship also shows that any position in calls can be synthetically replicated with puts and vice versa.
functions Formula
C − P = S − K·e^(-rT)
lightbulb Example
Stock at $100, 1-year call at strike $100 costs $10, risk-free rate 5%. PV of strike = $95.12. Put should cost: P = C − S + K·e^(-rT) = $10 − $100 + $95.12 = $5.12.
verified_user Key Points
- Fundamental arbitrage relationship for European options
- Violations create riskless profit opportunities
- Enables synthetic position construction
- Applies precisely to European options, approximately to American