Put-Call Parity
AdvancedPut-call parity is a principle that defines the relationship between the prices of European call and put options with the same underlying asset, exercise price and expiry date.
Put-call parity states that a call option plus the present value of the exercise price equals a put option plus the current price of the underlying asset. In other words, holding a call and enough cash to exercise it gives the same payoff as holding the share and a put.
This can be rearranged to find one option’s price from the other. For example, suppose a share trades at 100, the present value of the exercise price is 95 and the call option costs 12. Put-call parity implies the put should cost 12 plus 95 minus 100, or 7.
If prices move away from parity, traders can make risk-free profits through arbitrage, buying the cheaper combination and selling the more expensive one, which pushes prices back into line.
Put-call parity holds exactly for European options on assets that pay no dividends, and can be adjusted for dividends. It holds only approximately for American options, which can be exercised early. It is a useful check on option prices and helps traders build equivalent positions.
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