the total management fees under management in wall street is only 20 billion per year. so $3 billion in the options cboe casino is still a a lot of money to lose. that is what a options market makers said. the options market for equities is smaller than you think. I doubt there is any professional options market maker here to say otherwise. The CBOE clearing house has the answer.
I guess it depends on what numbers we are talking about: notional value, market maker haircut only, exchange only, including OTC, etc. Those numbers will be significantly different depending on what you include and how you calculate it. However your blind guess would not be in the ballpark, and I used to be a market maker on the CBOE.
Susquehanna (SIG) is prob the best in terms of institutional options traders (up there w/ citadel). very math/quant heavy and they understand risk/reward unlike the rest of wall street banks. prob b/c it's still a private company and if they lose money it comes directly out of their pockets not their stockholders.