What is "put-call parity"?

The principle that in an efficient market where no arbitrage opportunities exist, the market value of a synthetic portfolio consisting of a long stock and long put equals the market value of a long call and a long risk free bond which pays the strike price at expiration. The put and call must have the same underlying security, strike and expiration. The basic synthetic portfolio I mention can be re-arranged to solve for various long short combinations and the parity should hold (if not, it will be exploited until the market pricing corrects).
Basic Synthetic Formula:
C + X/RF = S + P
C
 
bostoncfa2014 wrote:The principle that in an efficient market where no arbitrage opportunities exist, the market value of a synthetic portfolio consisting of a long stock and long put equals the market value of a long call and a long risk free bond which pays the strike price at expiration. The put and call must have the same underlying security, strike and expiration. The basic synthetic portfolio I mention can be re-arranged to solve for various long short combinations and the parity should hold (if not, it will be exploited until the market pricing corrects).
Basic Synthetic Formula:
C + X/RF = S + P
Click to expand...
Additionally, the put option and the call option must be European options.
I’m not sure why you’re calling the two portfolios “synthetic”; one’s a protective put and the other is a fiduciary call, but there’s nothing synthetic about these portfolios. However, the relationship can be used to create synthetic securities: put options, call options, stocks, and bonds.
I wrote an article on put-call parity that may be of some help here: http://financialexamhelp123.com/put-call-parity/.
The definition, in layman’s terms, is that, because of arbitrage, if the price of a (European) put option changes by some amount, the price of a (European) call option (same underlying, strike price, and expiry as the put) has to change by exactly that same amount.
 
I must be subconsciously associating the synthetic terminology because of the protective put/fiduciary call/covered call concepts covered along w/ this. And forgot to stipulate European style - thanks S2000.
 
Bond + Call = Stock + Put
And all algebraic transformations of this are also true, so,
Bond = Stock + Put - Call, and
Put = Bond + Call - Stock, etc.
 
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