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GOODWILL, INTANGIBLE ASSETS, NET, AND DIGITAL ASSETS HELD - Goodwill by segment (Details) - USD ($)
$ in Millions
 3 Months Ended 12 Months Ended
May 02, 2022
Sep. 30, 2022
Jun. 30, 2022
Dec. 31, 2023
Dec. 31, 2022
Dec. 31, 2021
Goodwill            
Balance at beginning of the period       $ 3,122.8 $ 3,025.4  
Adjustment         4.4  
Additions         592.5  
Impairment         (460.9)  
Changes in foreign currency exchange rates       17.8 (38.6)  
Balance at end of the period       3,140.6 3,122.8 $ 3,025.4
Deferred tax benefit       15.2 155.7 18.9
Carrying value of investments       345.3 253.2  
Cboe Digital            
Goodwill            
Additions $ 460.9          
Impairment   $ (0.8) $ (460.1)      
Balance at end of the period   $ 0.0        
Deferred tax benefit     116.2      
Decrease in carrying value     343.9      
Carrying value of investments     220.0      
Intangible asset impairment     $ 0.0      
Other long lived assets $ 0.0          
Options            
Goodwill            
Balance at beginning of the period       305.8 305.8  
Balance at end of the period       305.8 305.8 305.8
North American Equities            
Goodwill            
Balance at beginning of the period       2,000.8 1,876.9  
Adjustment         0.2  
Additions         132.4  
Changes in foreign currency exchange rates       3.6 (8.7)  
Balance at end of the period       2,004.4 2,000.8 1,876.9
Europe and Asia Pacific            
Goodwill            
Balance at beginning of the period       549.0 575.5  
Adjustment         3.4  
Changes in foreign currency exchange rates       14.2 (29.9)  
Balance at end of the period       563.2 549.0 575.5
Global FX            
Goodwill            
Balance at beginning of the period       267.2 267.2  
Balance at end of the period       267.2 267.2 $ 267.2
Digital            
Goodwill            
Adjustment         0.8  
Additions         460.1  
Impairment         $ (460.9)  
Futures            
Goodwill            
Balance at end of the period       $ 0.0