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Is the Put-Call-Parity valid for binary (asset-or-nothing) options? If not, is there another formula for such exotic options?

I know that for regular options, there are arbitrage opportunities when the put-call-parity does not hold.


Please note that I am very new to learning finance and I am not looking for overly complex answers.

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the call version pays $$ I_{S_T > K } S_T $$ the put version pays $$ -I_{S_T < K } S_T $$

Subtract to get a pay-off $$ S_T. $$ (ignoring the probability zero event of $S_T=K.$)

So the prices subtract to give $S_0.$

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  • $\begingroup$ Is $$I_{S_T}$$ the indicator function? $\endgroup$ – Ryan J. Shrott Sep 1 '15 at 4:10
  • $\begingroup$ I understand how to price the options. Could you please clarify how your discussion is related to the Put-Call Parity. $\endgroup$ – Ryan J. Shrott Sep 1 '15 at 4:14
  • $\begingroup$ it shows that the call minus the put price is the stock price regardless of model. Is this not what you want? $\endgroup$ – Mark Joshi Sep 1 '15 at 5:17
  • $\begingroup$ @Ryan What Mark Joshi stated, he was trying to show you put-call parity works for all options. The parity is independent and can be applied to all kind of options. The version that you see in a text-book is simply a generalized version. $\endgroup$ – SmallChess Sep 1 '15 at 5:49

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