Put-call parity

Put-call parity is a no-arbitrage pricing relationship that defines the fair relationship between a call option, a put option, the underlying stock, and a risk-free bond , all with the same strike and expiration.

The relationship: Call price − Put price = Stock price − Present value of strike price

Why it matters: Put-call parity means that identical risk profiles can be replicated using different combinations of options and stock. If parity breaks down, arbitrageurs immediately exploit the discrepancy , which is why market prices stay very close to parity in practice.

Synthetic positions from put-call parity:

• Synthetic long stock = Long call + Short put (same strike)
• Synthetic short stock = Short call + Long put (same strike)
• Synthetic long call = Long put + Long stock
• Synthetic short put = Short call + Long stock (this is just a covered call)

Practical use: Understanding synthetic equivalents helps you replicate a desired exposure using a different combination of instruments , sometimes at lower cost or with more favorable tax treatment.

Why small deviations exist: The cost of carry (interest rates, dividends) creates small, predictable differences between call and put prices at the same strike. These are not arbitrage opportunities , they're built into the model.

Example: AAPL at $190. The $190 call costs $5.00. The $190 put costs $4.60. The $0.40 difference reflects the cost of carry (interest rates and expected dividends) , consistent with put-call parity.

Related terms: Intrinsic value, extrinsic value, synthetic position, call option, put option, interest rate (rho)

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