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

Question

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.

Mark Joshi · Accepted Answer · 2015-09-01 04:09:18Z

2

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 $S_0.$

answered Sep 1, 2015 at 4:09

Mark Joshi

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$\begingroup$ Is $$I_{S_T}$$ the indicator function? $\endgroup$
– Ryan J. Shrott
Sep 1, 2015 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, 2015 at 4:14
1

$\begingroup$ 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, 2015 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. $\endgroup$
– ABCD
Sep 1, 2015 at 5:49

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