Long collar / Short collar

Long collar = long put + short call
Is this correct??

Protective put + Sell OTM Call

On top of your long position in the underlying: yes.

A collar (by default) is with ATM or OTM call and put options? It seems there are contradictory definition on this strategy.

Sometimes the question can be more explicit saying “zero cost collar”, but sometimes a collar then you have either a ATM call + ATM put or OTM call + OTM call…

The curriculum usually uses an OTM call and an OTM put.

That’s not a collar; it’s a synthetic long or a synthetic short.

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Would it make a difference if the question specifies its for an “overlay” strategy? Then either a synthetic long/short collar makes more sense ?

Nope.

In a synthetic long or a synthetic short, the call option and the put option have the same strike price.

In a collar the put option has a lower strike price than the call option.

Great, thanks!

My pleasure.