Put-Call Parity – Defined and Simplified

Cole Turner

The put-call parity is the relationship that exists between put and call prices of the same underlying security, strike price, and expiration month.

The put-call parity is important because it eliminates the possibility of arbitrage traders making profitable trades with no risk. This article will explain what arbitrage is, what the put-call parity is, and how the put-call parity eliminates arbitrage.

Arbitrage is the opportunity to profit from price variances in a financial security in different markets. For example, an arbitrage opportunity would be if an investor bought Stock XYZ in one market for $30 while simultaneously selling Stock XYZ in a different market for $40. These synchronized trades would give a profit of $10 to the investor with virtually no risk.

When prices diverge, as in the case with arbitrage opportunities, the selling pressure in the higher-priced market drives prices down while the buying pressure in the lower-priced market drives prices up.

The buying and selling pressure in the two different markets brings the prices back together eliminating any arbitrage opportunities. This pressure to bring the prices back together is the put-call parity.

The formula for the put-call parity is ‘Call – Put = Stock – Strike.’ For example, assume Stock XYZ was trading at $50 and the option strike prices were $45. The premium for the call option would be $7 while the put option is $2. This is the put-call parity in action as (7 – 2 = 50 – 45).

By understanding the put-call parity formula, an investor can connect the value between a put option, call option, and underlying security, as long as the put and call have the same strike price and expiration date. Because of this, the put-call parity eliminates arbitrage opportunities from happening.

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