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GOODWILL, INTANGIBLE ASSETS, NET, AND DIGITAL ASSETS HELD - Intangible assets by category (Details) - USD ($)
$ in Millions
Sep. 30, 2023
Dec. 31, 2022
Intangible Assets    
Intangible assets, net $ 1,571.3 $ 1,662.8
Customer relationships | Weighted Average    
Intangible Assets    
Amortization period (in years) 15 years 16 years
Market data customer relationships | Weighted Average    
Intangible Assets    
Amortization period (in years) 9 years 9 years
Technology | Weighted Average    
Intangible Assets    
Amortization period (in years) 7 years 8 years
Trademarks and tradenames | Weighted Average    
Intangible Assets    
Amortization period (in years) 6 years 7 years
Options    
Intangible Assets    
Accumulated amortization $ (99.6) $ (90.6)
Intangible assets, net 137.1 146.1
Options | Customer relationships    
Intangible Assets    
Finite-lived intangible assets, gross 46.6 46.6
Options | Market data customer relationships    
Intangible Assets    
Finite-lived intangible assets, gross 53.6 53.6
Options | Technology    
Intangible Assets    
Finite-lived intangible assets, gross 28.1 28.1
Options | Trademarks and tradenames    
Intangible Assets    
Finite-lived intangible assets, gross 12.9 12.9
Options | Trading registrations and licenses    
Intangible Assets    
Indefinite-lived intangible assets, gross 95.5 95.5
North American Equities    
Intangible Assets    
Accumulated amortization (456.6) (411.9)
Intangible assets, net 947.9 992.8
North American Equities | Customer relationships    
Intangible Assets    
Finite-lived intangible assets, gross 412.6 412.8
North American Equities | Market data customer relationships    
Intangible Assets    
Finite-lived intangible assets, gross 322.0 322.0
North American Equities | Technology    
Intangible Assets    
Finite-lived intangible assets, gross 56.5 56.4
North American Equities | Trademarks and tradenames    
Intangible Assets    
Finite-lived intangible assets, gross 8.2 8.2
North American Equities | Trading registrations and licenses    
Intangible Assets    
Indefinite-lived intangible assets, gross 605.2 605.3
Europe and Asia Pacific    
Intangible Assets    
Accumulated amortization (159.3) (142.0)
Intangible assets, net 341.0 359.9
Europe and Asia Pacific | Customer relationships    
Intangible Assets    
Finite-lived intangible assets, gross 206.0 208.9
Europe and Asia Pacific | Market data customer relationships    
Intangible Assets    
Finite-lived intangible assets, gross 58.9 58.4
Europe and Asia Pacific | Technology    
Intangible Assets    
Finite-lived intangible assets, gross 33.0 32.8
Europe and Asia Pacific | Trademarks and tradenames    
Intangible Assets    
Finite-lived intangible assets, gross 2.3 2.3
Europe and Asia Pacific | Trading registrations and licenses    
Intangible Assets    
Indefinite-lived intangible assets, gross 200.1 199.5
Global FX    
Intangible Assets    
Accumulated amortization (167.9) (155.3)
Intangible assets, net 60.2 72.8
Global FX | Customer relationships    
Intangible Assets    
Finite-lived intangible assets, gross 140.0 140.0
Global FX | Market data customer relationships    
Intangible Assets    
Finite-lived intangible assets, gross 64.4 64.4
Global FX | Technology    
Intangible Assets    
Finite-lived intangible assets, gross 22.5 22.5
Global FX | Trademarks and tradenames    
Intangible Assets    
Finite-lived intangible assets, gross 1.2 1.2
Digital    
Intangible Assets    
Accumulated amortization (10.0) (4.7)
Intangible assets, net 85.1 91.2
Digital | Technology    
Intangible Assets    
Finite-lived intangible assets, gross 70.0 70.0
Digital | Trading registrations and licenses    
Intangible Assets    
Indefinite-lived intangible assets, gross 25.0 25.0
Digital | Digital assets held    
Intangible Assets    
Indefinite-lived intangible assets, gross $ 0.1 $ 0.9