The put-call parity equation
Call + PV(Strike) = Put + Stock
When apparent parity violations appear
If this equation doesn’t hold, there’s an arbitrage opportunity. In practice, market makers enforce parity within fractions of a cent. When you see apparent violations, they’re usually explained by dividends, borrowing costs, or American exercise features.
Synthetic positions from rearranging parity
| Rearrangement | Synthetic Position | Use Case |
|---|---|---|
| Call = Put + Stock − PV(K) | Synthetic long call | When calls are mispriced relative to puts |
| Put = Call − Stock + PV(K) | Synthetic long put | When puts are mispriced relative to calls |
| Stock = Call − Put + PV(K) | Synthetic stock | Replicate stock exposure using options |
Check parity holds on a real chain
Pick a stock and check the prices of a call and put at the same strike and expiration. Verify that put-call parity approximately holds: Call − Put ≈ Stock − PV(Strike).
Testing whether parity holds
A $100 call costs $8 and the corresponding $100 put costs $5. The stock is at $103. Does put-call parity approximately hold?
Why one option's price fixes the other
Spotting arbitrage when parity breaks
Put-call parity says: Call - Put = Stock - PV(Strike). If a call is trading at $5, same-strike put at $3, stock at $100, and PV of $100 strike is $98, is there an arbitrage?
Check your understanding
Sit with the ideas.
A stock trades at $100. A $100-strike call costs $8.00 and a $100-strike put costs $6.50, both expiring in one year. The risk-free rate is 3%. Does put-call parity hold?
Why: