If I hold a long and a short position on the same option, do the contracts cancel out each other?
Suppose I sold an option on stock X, with strike price Y, and expiry date Z. Suppose I later buy an option on the same stock, with the same strike price, and the same expiry date. Do these two positions cancel out each other (i.e. both contracts cease to exist anywhere), or will I end up with two separate contracts?
Is it the same with the reverse situation? e.g. I bought an option on stock A, with strike price B, and expiry date C. If I later sell an option on the same stock, with the same strike price and expiry date, will I end up with two contracts (one long position, one short position)?
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Assuming that both options are the same type (i.e. put or call) then yes, they cancel each other out.
If you initially sold the option, then bought the same option (same underlying, strike, type, and expiry), this is called buy to close. You close out your position, and the "clearing house" cancels out the two contracts.
Is it the same with the reverse situation?
Yes.
When you establish a new option position it is either:
Buy to Open (BTO) or Sell To Open (STO)
When you close an existing option position it is either:
Buy To Close (BTC) or Sell To Close (STC)
A closing position cancels an opening position. IOW:
BTO + STC = no position
STO + BTC = no position
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