what is put call parity 
put call parity is a foundational principle in options pricing theory it states that the price of a call option implies a specific fair price for the corresponding put option with the same strike price and expiration date and vice versa if market prices diverge from this relationship it signals a mispricing that shrewd traders know to exploit for profit however in general modern trading systems make it so that these rarely occur 1put call parity which only applies to european options can be determined by a set equation we ll break down the precise definition and formula illustrate step by step how it works and walk through concrete examples by the end you ll grasp this core options pricing principle and how to apply it in real world trading scenarios investopedia laura porterunderstanding put call parityput call parity is a fundamental principle in options pricing that defines the relationship between the price of a european call option and a european put option with the same underlying asset strike price and expiration date in essence it states that holding a portfolio of a long call option and a short put option or vice versa should yield the same return as having one share of the underlying stock assuming certain conditions are met alternatively it also means that simultaneously holding a short european put and long european call of the same class will deliver the same return as holding one forward contract on the same underlying asset with the same expiration and a forward price equal to the option s strike price 2the equation that expresses put call parity is as follows 3c p v x p s where c price of the european call option p v x present value of the strike price x discounted from the value on the expiration date at the risk free rate p price of the european put s spot price or the current market value of the underlying asset begin aligned c pv x p s textbf where c text price of the european call option pv x text present value of the strike price x text discounted from the value on the expiration text date at the risk free rate p text price of the european put s text spot price or the current market value text of the underlying asset end aligned c pv x p swhere c price of the european call optionpv x present value of the strike price x discounted from the value on the expirationdate at the risk free ratep price of the european puts spot price or the current market valueof the underlying asset economist hans r stoll introduced the put call parity concept in his 1969 paper the relationship between put and call option prices published in the journal of finance 4if this equation holds the options market is in equilibrium with no arbitrage prospects available however if the prices of the put and call options diverge from the value predicted by put call parity one exists traders can exploit this mispricing by simultaneously buying the underpriced option and selling the overpriced option locking in a risk free profit put call parity plays a crucial role in options pricing and risk management market makers and traders rely on put call parity models to identify mispricing and maintain efficient markets sophisticated trading algorithms and pricing models use put call parity as a fundamental building block this also means most developed markets see few chances for trading on related arbitrage situations however real world factors like transaction costs taxes dividend risks and liquidity constraints can cause option prices to deviate slightly from the theoretical values predicted by put call parity empirical studies have found that while put call parity generally holds in most markets there can be brief periods of disequilibrium especially during times of high market volatility or illiquidity 15for individual investors understanding put call parity is important for making informed decisions about options trading strategies investors can identify potential mispricings and trading prospects by monitoring the relationship between put and call prices however individual investors should be cautious about relying only on put call parity as the transaction costs of executing an arbitrage trade can often outweigh the potential profits example of put call parityassume that we want to know if the price of a six month european 55 strike put option on xyz stock at 7 46 is correct given the following information plugging these into the equation above therefore the price of the six month european put option on xyz stock should be 7 46 according to the put call parity principle since it is parity is in place in this situation 