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FAIR VALUE MEASUREMENT - Fair value hierarchy for assets and liabilities (Details) - USD ($)
$ in Millions
Jun. 30, 2024
Dec. 31, 2023
Assets:    
Total assets $ 97.0 $ 108.9
Digital assets - safeguarded assets 6.9 51.3
Note receivable - building sale 6.4  
Liabilities:    
Contingent consideration liabilities 1.8 11.8
Digital assets - safeguarded liabilities 6.9 51.3
Cboe Digital restricted common units liability   18.7
Cboe Digital warrant liability   5.9
Total liabilities 1,339.4 1,430.1
Level 1    
Assets:    
Total assets 83.7 57.6
Liabilities:    
Total liabilities 36.6 36.7
Level 2    
Assets:    
Total assets 6.9 51.3
Digital assets - safeguarded assets 6.9 51.3
Liabilities:    
Digital assets - safeguarded liabilities 6.9 51.3
Total liabilities 1,301.0 1,357.0
Level 3    
Assets:    
Total assets 6.4  
Note receivable - building sale 6.4  
Liabilities:    
Contingent consideration liabilities 1.8 11.8
Cboe Digital restricted common units liability   18.7
Cboe Digital warrant liability   5.9
Total liabilities 1.8 36.4
Recurring    
Assets:    
Total assets 97.0 108.8
Digital assets - safeguarded assets 6.9 51.3
Note receivable - building sale 6.4  
Liabilities:    
Contingent consideration liabilities 1.8 11.8
Digital assets - safeguarded liabilities 6.9 51.3
Cboe Digital restricted common units liability   18.7
Cboe Digital warrant liability   5.9
Total liabilities 8.7 87.7
Recurring | U.S. Treasury securities    
Assets:    
Total assets 47.1 20.8
Recurring | Marketable securities | Mutual funds    
Assets:    
Total assets 18.8 17.1
Recurring | Marketable securities | Money market funds    
Assets:    
Total assets 17.8 19.6
Recurring | Level 1    
Assets:    
Total assets 83.7 57.5
Recurring | Level 1 | U.S. Treasury securities    
Assets:    
Total assets 47.1 20.8
Recurring | Level 1 | Marketable securities | Mutual funds    
Assets:    
Total assets 18.8 17.1
Recurring | Level 1 | Marketable securities | Money market funds    
Assets:    
Total assets 17.8 19.6
Recurring | Level 2    
Assets:    
Total assets 6.9 51.3
Digital assets - safeguarded assets 6.9 51.3
Liabilities:    
Digital assets - safeguarded liabilities 6.9 51.3
Total liabilities 6.9 51.3
Recurring | Level 3    
Assets:    
Total assets 6.4  
Note receivable - building sale 6.4  
Liabilities:    
Contingent consideration liabilities 1.8 11.8
Cboe Digital restricted common units liability   18.7
Cboe Digital warrant liability   5.9
Total liabilities $ 1.8 $ 36.4