Yes, there are multiple exchanges for trading options in the United States:
- CBOE (Cboe Options Exchange, Incorporated) "CBOE" or "C1"
- C2 (Cboe C2 Options Exchange, Incorporated) "C2"
- BATS (Cboe BZX Options Exchange, Inc.) "BATS Options"
- EDGX (Cboe EDGX Options Exchange, Inc.) "EDGX Options"
- MIAX (Miami International Securities Exchange, LLC) "MIAX"
- EMLD (MIAX Emerald, LLC) "MIAX Emerald"
- PEARL (MIAX PEARL, LLC) "MIAX Pearl"
- NSDQ (The Nasdaq Stock Market LLC) "The NASDAQ Options Market"
- NOBO (Nasdaq BX, Inc.) "NASDAQ OMX BX Options"
- MCRY (Nasdaq MRX, LLC) "NASDAQ ISE Mercury"
- PHLX (Nasdaq PHLX LLC) "The Philadelphia Options Exchange"
- ISE (Nasdaq ISE, LLC) "The International Securities Exchange"
- GEM (Nasdaq GEMX, LLC) "ISE Gemini"
- AMEX (NYSE American LLC) "NYSE Amex Options"
- ARCA (NYSE Arca, Inc.) "NYSE Arca Options"
- BOX (BOX Options Exchange LLC) "The Boston Options Exchange"
Note: the name is quotes is what I would call it, but that is probably a prior name. They frequently change as the companies owning them go through restructuring and sell them on.
Clarification
To clarify, we are talking out the original CBOE Options Exchange (sometimes called C1):
Other than being the largest options exchange, does the CBOE have any special role in the US options market?
No. If CBOE disappeared tomorrow, the market wouldn't blink. In fact sometimes an exchange may be offline for hours due to some mundane technical problem (e.g. first thing on Monday after a software upgrade) and there is little impact. Few participants trade only on CBOE without access to any other platform to execute a trade.
Who gets to create new option chains or contracts (e.g. new expiry dates, new strike prices, etc.)?
Any options exchange can list a new 'class' of options but they usually need a market maker willing to provide continuous quotations in that options class. Market makers sometimes ask exchanges if they can list a new options class, and sometimes exchanges (presumably due to member request) ask market makers if they can do the same.
Exchanges usually add new expirations and strikes in line with their own listing rules or sometimes on the request of a participant.
If an options exchange lists a new series intraday, typically every other options will pick it up and list it on their system the next day.
Can any options exchange create new options chains or contracts at any time?
The exchanges have their own listing criteria specified in their rulebook. There has been pushback from market makers on exchanges adding too many strikes (each strike takes up system capacity) so they are less liberal than they used to be. There have been instances where an exchange has listed extra options 'by mistake', which in turn have been copied by other exchanges the next day, and a subsequent attempt by the exchanges to remove the strikes. Some exchanges now have a 'close only' designation on certain series to try to remove them prior to expiration, where they will only allow the order if the order will reduce an existing position (i.e. decrease the open interest).
Is the options market similar to the stock market in that there is a single "listing exchange" for each chain or contract, but many "trading exchanges"? Or are there only "trading exchanges"?
I think the "listing" responsibilities are handled by the OCC, so there is no special designation for a security listed on one exchange and not another.