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Put-Call Parity

The put-call parity is useful as part of a hedging/ speculative strategy for a trader who wants to participate in the futures market. The put-call parity explains the relationship between the prices of put and call options in the same category--in other words, options with the same strike price, expiration date and underlying price.

In general, the value of a put option implies a fair value for the corresponding call, and vice versa. Thus, the price of one option cannot move very far without the price of the corresponding option changing accordingly. The parity is violated when there is a large price difference between the put and call options. Although the parity concept is strictly confined to European options, the relationship is applicable to American options as well (adjusting for dividends and interest rates).

From a trading perspective, the put-call parity reveals an arbitrage opportunity if there is a divergence between the value of calls and puts in the same category--in other words, if the parity is violated. If an option pricing model that produces put and call prices does not satisfy the parity, it can open up arbitrage opportunities. Arbitrageurs can profit until the gap between the put and call narrows. Although arbitrage strategies are not considered useful for the average trader, the corresponding synthetic relationship in the options market can reveal trading strategies. Conversion and reversal strategies are the most commonly used arbitrage techniques that profit from the put-call parity.

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