My question concerns an ambiguity in the wikipedia article about Put Call Parity.
In the first sentence: "In financial mathematics, put–call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to (and hence has the same value as) a single forward contract at this strike price and expiry."
is about a "short" put option which means that we have the obligation to sell the put but in the derivation a long put is used, i.e. a put with payoff profile $(K - S_T, 0)^+$. But a short put would be actually $K-S_T \in \mathbb{R}$ if the option gets exercised.
Edit: My question concerns the definition of "short put". In http://www.investopedia.com/terms/s/short-put.asp it is definied as the obligation to sell and then its not the payoff: $-(K-S_T)^+$?


closed as off-topic by LocalVolatility, amdopt, msitt, zer0hedge, olaker Jun 14 '17 at 18:00

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  • $\begingroup$ You don't "have the obligation to sell the put", you have already sold it so now your payoff is the negative of the payoff of a put. $\endgroup$ – noob2 May 31 '17 at 13:32

Being short a put simply means that you have sold the put, hence its payoff is from your point of view $-(K - S_T)^+$. When your are long a call and short a put your total payoff is $(S_T - K)^+ -(K - S_T)^+ = S_T - K$, hence the call/put parity.


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