Put Call Parity Calculator

Understanding Put-Call Parity

Put-Call Parity is a fundamental principle in options pricing theory that defines the static equilibrium relationship between European call option prices, European put option prices, the underlying asset spot price, and the present value of the strike price.

The Put-Call Parity Equation

For European-style options on a non-dividend-paying asset, the core put-call parity relationship is expressed as:

$$C + K \cdot e^{-rT} = P + S$$

Where:

• $C$: European Call Option Price
• $P$: European Put Option Price
• $S$: Current Spot Price of the Underlying Asset
• $K$: Strike Price (Exercise Price)
• $r$: Annual Risk-Free Interest Rate
• $T$: Time to Expiration (in years)

Fiduciary Call vs. Protective Put

Put-call parity is established by comparing two financial portfolios that guarantee identical payoffs at option expiration:

1. Fiduciary Call Portfolio: Buying a European call option plus investing the present value of the strike price in a zero-coupon risk-free bond ($C + K \cdot e^{-rT}$).
2. Protective Put Portfolio: Buying a European put option plus purchasing one share of the underlying asset ($P + S$).

Because both portfolios yield exactly $\max(S_T, K)$ at expiration date $T$, their market prices must be identical today to prevent riskless arbitrage opportunities.