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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, 2022
Dec. 31, 2021
Dec. 31, 2020
Goodwill            
Balance at beginning of the period       $ 3,025.4 $ 2,895.1  
Adjustment       4.4 (0.9)  
Additions       592.5 134.0  
Impairment       (460.9)    
Changes in foreign currency exchange rates       (38.6) (2.8)  
Balance at end of the period       3,122.8 3,025.4 $ 2,895.1
Deferred tax benefit       155.7 18.9 30.9
Carrying value       253.2 245.8  
Cboe Digital            
Goodwill            
Additions $ 460.9          
Impairment   $ (0.8)        
Options            
Goodwill            
Balance at beginning of the period       305.8 305.8  
Adjustment       0.0 0.0  
Additions       0.0 0.0  
Impairment       0.0    
Changes in foreign currency exchange rates       0.0 0.0  
Balance at end of the period       305.8 305.8 305.8
North American Equities            
Goodwill            
Balance at beginning of the period       1,876.9 1,877.3  
Adjustment       0.2 (0.5)  
Additions       132.4 0.0  
Impairment       0.0    
Changes in foreign currency exchange rates       (8.7) 0.1  
Balance at end of the period       2,000.8 1,876.9 1,877.3
Europe and Asia Pacific            
Goodwill            
Balance at beginning of the period       575.5 444.8  
Adjustment       3.4 (0.4)  
Additions       0.0 134.0  
Impairment       0.0    
Changes in foreign currency exchange rates       (29.9) (2.9)  
Balance at end of the period       549.0 575.5 444.8
Global FX            
Goodwill            
Balance at beginning of the period       267.2 267.2  
Adjustment       0.0 0.0  
Additions       0.0 0.0  
Impairment       0.0    
Changes in foreign currency exchange rates       0.0 0.0  
Balance at end of the period       267.2 267.2 267.2
Digital            
Goodwill            
Balance at beginning of the period       0.0 0.0  
Adjustment       0.8 0.0  
Additions       460.1 0.0  
Impairment     $ 460.1 (460.9)    
Changes in foreign currency exchange rates       0.0 0.0  
Balance at end of the period       0.0 $ 0.0 $ 0.0
Deferred tax benefit     116.2      
Decrease in carrying value     343.9      
Carrying value     220.0      
Intangible asset impairment     $ 0.0      
Other long lived assets $ 0.0          
Futures            
Goodwill            
Balance at end of the period       $ 0.0