# Put-Call Parity Arbitrage Exploitation for Binary-Asset-or-Nothing Options

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.

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 $S_0.$

• Is $$I_{S_T}$$ the indicator function? – Ryan J. Shrott Sep 1 '15 at 4:10
• I understand how to price the options. Could you please clarify how your discussion is related to the Put-Call Parity. – Ryan J. Shrott Sep 1 '15 at 4:14
• it shows that the call minus the put price is the stock price regardless of model. Is this not what you want? – Mark Joshi Sep 1 '15 at 5:17
• @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. – SmallChess Sep 1 '15 at 5:49