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GOODWILL, INTANGIBLE ASSETS, NET, AND DIGITAL ASSETS HELD - Goodwill by segment (Details) - USD ($)
$ in Millions
 6 Months Ended
Jun. 30, 2024
Dec. 31, 2023
Goodwill    
Balance at beginning of the period $ 3,140.6  
Changes in foreign currency exchange rates (7.7)  
Balance at end of the period 3,132.9  
Carrying value of investments 359.5 $ 345.3
Options    
Goodwill    
Balance at beginning of the period 305.8  
Balance at end of the period 305.8  
North American Equities    
Goodwill    
Balance at beginning of the period 2,004.4  
Changes in foreign currency exchange rates (5.2)  
Balance at end of the period 1,999.2  
Europe and Asia Pacific    
Goodwill    
Balance at beginning of the period 563.2  
Changes in foreign currency exchange rates (2.5)  
Balance at end of the period 560.7  
Global FX    
Goodwill    
Balance at beginning of the period 267.2  
Balance at end of the period 267.2  
Futures    
Goodwill    
Balance at end of the period $ 0.0