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GOODWILL, INTANGIBLE ASSETS, NET, AND DIGITAL ASSETS HELD - Goodwill by segment (Details) - USD ($)
$ in Millions
 3 Months Ended 6 Months Ended
Jun. 30, 2022
Jun. 30, 2022
Jun. 30, 2021
Dec. 31, 2021
Goodwill        
Balance at beginning of the period   $ 3,025.4    
Adjustment   3.4    
Additions   592.5    
Impairment $ (460.1) (460.1)    
Changes in foreign currency exchange rates   (29.2)    
Balance at end of the period 3,132.0 3,132.0    
Deferred tax benefit   142.3 $ (5.9)  
Carrying value 243.5 243.5   $ 245.8
Options        
Goodwill        
Balance at beginning of the period   305.8    
Balance at end of the period 305.8 305.8    
North American Equities        
Goodwill        
Balance at beginning of the period   1,876.9    
Additions   132.4    
Changes in foreign currency exchange rates   (0.5)    
Balance at end of the period 2,008.8 2,008.8    
Europe and Asia Pacific        
Goodwill        
Balance at beginning of the period   575.5    
Adjustment   3.4    
Changes in foreign currency exchange rates   (28.7)    
Balance at end of the period 550.2 550.2    
Global FX        
Goodwill        
Balance at beginning of the period   267.2    
Balance at end of the period 267.2 267.2    
Digital        
Goodwill        
Additions   460.1    
Impairment 460.1 (460.1)    
Deferred tax benefit 116.2      
Decrease in carrying value 343.9 343.9    
Carrying value 220.0 220.0    
Intangible asset impairment   0.0    
Futures        
Goodwill        
Balance at end of the period $ 0.0 $ 0.0