The fundamental no-arbitrage relationship between call and put option prices on the same underlying, strike, and expiry: C − P = S − PV(K).
PrepClever Glossary · Derivatives
updateUpdated July 2026
Formula
C − P = S − PV(K) where PV(K) = K × e^(−rT)
Put-Call Parity states that for European options on a non-dividend-paying stock:
C − P = S − PV(K) = S − Ke-rT
If this relationship is violated, a riskless arbitrage profit exists.
Put-call parity allows creating synthetic positions:
Example
Nifty = 23,000. Strike = 23,000. Expiry = 30 days. Rf = 7%. PV(K) = 23,000 × e^(−0.07×30/365) = 22,868. So C − P should equal 23,000 − 22,868 = 132. If Nifty 23,000 Call = ₹300 and Put = ₹180, C − P = 120 ≠ 132. Slight arbitrage opportunity exists.
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