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FAIR VALUE MEASUREMENT - Fair value hierarchy for assets and liabilities (Details) - USD ($)
$ in Millions
Dec. 31, 2023
Dec. 31, 2022
Jun. 30, 2022
Assets:      
Total assets $ 108.9 $ 115.5  
Digital assets - safeguarded assets 51.3 22.9 $ 22.4
Liabilities:      
Contingent consideration liabilities 11.8 39.1  
Digital assets - safeguarded liabilities 51.3 22.9 $ 22.4
Cboe Digital restricted common units liability 18.7 15.5  
Cboe Digital warrant liability 5.9 5.9  
Total liabilities 1,430.1 1,684.8  
Level 1      
Assets:      
Total assets 57.6 115.5  
Digital assets - safeguarded assets   22.9  
Liabilities:      
Digital assets - safeguarded liabilities   22.9  
Total liabilities 36.7 50.4  
Level 2      
Assets:      
Total assets 51.3    
Digital assets - safeguarded assets 51.3    
Liabilities:      
Digital assets - safeguarded liabilities 51.3    
Total liabilities 1,357.0 1,573.9  
Level 3      
Liabilities:      
Contingent consideration liabilities 11.8 39.1  
Cboe Digital restricted common units liability 18.7 15.5  
Cboe Digital warrant liability 5.9 5.9  
Total liabilities 36.4 60.5  
Recurring      
Assets:      
Total assets 108.8 114.6  
Digital assets - safeguarded assets 51.3 22.9  
Liabilities:      
Contingent consideration liabilities 11.8 39.1  
Digital assets - safeguarded liabilities 51.3 22.9  
Cboe Digital restricted common units liability 18.7 15.5  
Cboe Digital warrant liability 5.9 5.9  
Total liabilities 87.7 83.4  
Recurring | U.S. Treasury securities      
Assets:      
Total assets 20.8 64.2  
Recurring | Marketable securities | Mutual funds      
Assets:      
Total assets 17.1 15.3  
Recurring | Marketable securities | Money market funds      
Assets:      
Total assets 19.6 12.2  
Recurring | Level 1      
Assets:      
Total assets 57.5 114.6  
Digital assets - safeguarded assets   22.9  
Liabilities:      
Digital assets - safeguarded liabilities   22.9  
Total liabilities   22.9  
Recurring | Level 1 | U.S. Treasury securities      
Assets:      
Total assets 20.8 64.2  
Recurring | Level 1 | Marketable securities | Mutual funds      
Assets:      
Total assets 17.1 15.3  
Recurring | Level 1 | Marketable securities | Money market funds      
Assets:      
Total assets 19.6 12.2  
Recurring | Level 2      
Assets:      
Total assets 51.3    
Digital assets - safeguarded assets 51.3    
Liabilities:      
Digital assets - safeguarded liabilities 51.3    
Total liabilities 51.3    
Recurring | Level 3      
Liabilities:      
Contingent consideration liabilities 11.8 39.1  
Cboe Digital restricted common units liability 18.7 15.5  
Cboe Digital warrant liability 5.9 5.9  
Total liabilities $ 36.4 $ 60.5