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What is Put-Call Parity?
Put-Call Parity is a fundamental concept in options pricing theory that establishes a relationship between the prices of call options and put options with the same underlying asset, strike price, and expiration date. It is based on the principle that the value of a call option plus the present value of the strike price equals the value of a put option plus the current price of the underlying asset.
The put-call parity equation can be expressed as follows:
C + PV(K) = P + S
Where:
- C is the price of the call option
- PV(K) is the present value of the strike price (K) discounted to the present time
- P is the price of the put option
- S is the current price of the underlying asset
The put-call parity equation holds under the assumptions of no arbitrage and efficient markets. It implies that the combination of a long call option and a short put option, both with the same strike price and expiration date, should have the same value as holding the underlying asset.
Put-call parity has several implications and applications in options trading and risk management. It allows for the determination of the theoretical prices of options based on the prices of other options and the underlying asset. Any deviation from put-call parity could create arbitrage opportunities, where traders can exploit mispricing by executing a combination of trades to make risk-free profits. Put-call parity is also used for options pricing models, such as the Black-Scholes model, as it provides a consistency check on the model's assumptions and output. It is a fundamental concept for options traders and analysts, helping them assess the fair value of options and construct hedging or trading strategies.
However, it's important to note that put-call parity assumes ideal market conditions, including no transaction costs, no restrictions on short selling, no dividend payments, and no market frictions. Deviations from these assumptions or the presence of market imperfections can lead to temporary violations of put-call parity. Traders closely monitor such deviations and take advantage of potential arbitrage opportunities to restore equilibrium.