what about a mismatch in put call prices 
in the above we can see that the put call parity equation is satisfied as the prices of the call option put option underlying stock and the present value of the strike price are in equilibrium the equation shows no arbitrage chances are available because the relationship between the prices is balanced however if there were a mismatch in the equation it would suggest an arbitrage opportunity for instance let s say the market price of the put option p is actually 8 00 instead of 7 46 in this case the equation would look like 3 54 46 8 50 57 46 58this means the put option is overpriced relative to the call option and the underlying stock an arbitrageur could exploit this mispricing by selling the put option for 8 buying the call option for 3 and shorting the underlying stock at 50 this would result in an immediate cash inflow of 5 8 3 at expiration the arbitrageur would have a guaranteed profit of 0 54 57 46 57 because the short stock position would cancel out the exercise of either the put or call option put call parity and arbitrageas we ve seen when one side of the put call parity equation is greater than the other this is an arbitrage opportunity you can sell the more expensive side of the equation and buy the cheaper side to make for all intents and purposes a risk free profit 6in practice this means selling a put shorting the stock buying a call and buying a risk free asset tips for example in reality prospects for arbitrage are short lived and difficult to find in addition their margins may be so thin that an enormous amount of capital is required to take advantage of them investopedia sabrina jiangin the graph above the y axis represents the value of the portfolio the prices of european put and call options are ultimately governed by put call parity 6 in a theoretical perfectly efficient market the prices for european put and call options would be governed by the equation above c p v x p s begin aligned c pv x p s end aligned c pv x p s let s say that the risk free rate is 4 and that tckr stock trades at 10 let s ignore transaction fees and assume tckr doesn t pay dividends for tckr options expiring in one year with a strike price of 15 we have as follows c 15 1 04 p 10 4 42 p c begin aligned c 15 div 1 04 p 10 4 42 p c end aligned c 15 1 04 p 104 42 p c tckr would trade at a 4 42 premium to their corresponding calls in this hypothetical market with tckr trading at just 67 of the strike price the bullish call seems to have the longer odds which makes intuitive sense let s say this is not the case and for whatever reason the puts are trading at 12 the calls at 7 suppose you purchase a european call option for tckr stock the expiration date is one year from now the strike price is 15 and buying the call costs you 5 this contract gives you the right but not the obligation to acquire tckr stock on the expiration date for 15 whatever the market price if one year from now tckr trades at 10 you won t exercise the option however if tckr is trading at 20 per share you will exercise the option buy tckr at 15 and break even since you paid 5 for the option any amount tckr rises above 20 is pure profit assuming there aren t any transaction fees 7 14 42 12 10 21 42 fiduciary call 22 protected put begin aligned 7 14 42 12 10 21 42 text fiduciary call 22 text protected put end aligned 7 14 42 12 1021 42 fiduciary call 22 protected put another way to imagine put call parity is to compare the performance of a protective put and a fiduciary call of the same class a protective put is a long stock position combined with a long put which limits the potential downside of holding the stock investopedia sabrina jianga fiduciary call is an investment strategy combining a long call option position with a risk free asset such as a treasury bill or cash to ensure the investor has enough funds to exercise the call option at expiration the amount of the risk free asset is equal to the present value of the strike price adjusted for the discount rate over the option s lifetime let s continue with the example assuming that the tckr puts and calls with a strike price of 15 expire in one year trade for free you could create a fiduciary call by holding the following suppose the risk free interest rate is 5 a year the present value of the 15 strike price can be calculated as follows present value future value 1 discount rate timepresent value 15 1 0 05 1 14 29in this case you would hold the long call option and 14 29 in cash at expiration if the stock price is above 15 you will use the 14 29 in cash to exercise the call option and buy the stock at 15 if the stock price is below 15 the call option will expire worthless and you ll keep the 14 29 in cash the fiduciary call strategy ensures investors have enough funds to exercise the call option at expiration eliminating the need to provide additional cash or sell other assets this strategy is like holding the underlying stock outright but limits the downside risk to the present value of the strike price however it s essential to note that in reality call options are not traded for free and the cost of the option premium must be considered when implementing this strategy investopedia sabrina jiangcan put call parity be used with american options put call parity is most straightforward with european options because they can only be exercised at expiration however while american options can be exercised at any time before expiration the put call parity relationship still holds under certain conditions the primary difference is that the flexibility of early exercise in american options can create scenarios where the parity relationship needs adjustments to account for potential dividends and the early exercise premium despite these complexities the fundamental principle of put call parity is a foundation for understanding the relationship between puts calls and the underlying asset 4