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FAIR VALUE MEASUREMENT - Fair value hierarchy for assets and liabilities (Details) - USD ($)
$ in Millions
Sep. 30, 2023
Dec. 31, 2022
Assets:    
Total assets $ 74.3 $ 115.5
Digital assets - safeguarded assets 40.2 22.9
Liabilities:    
Contingent consideration liabilities 28.2 39.1
Digital assets - safeguarded liabilities 40.2 22.9
Cboe Digital restricted common units liability 18.7 15.5
Cboe Digital warrant liability 5.9 5.9
Total liabilities 1,438.0 1,684.8
Level 1    
Assets:    
Total assets 74.3 115.5
Digital assets - safeguarded assets 40.2 22.9
Liabilities:    
Digital assets - safeguarded liabilities 40.2 22.9
Total liabilities 73.7 50.4
Level 2    
Liabilities:    
Total liabilities 1,311.5 1,573.9
Level 3    
Liabilities:    
Contingent consideration liabilities 28.2 39.1
Cboe Digital restricted common units liability 18.7 15.5
Cboe Digital warrant liability 5.9 5.9
Total liabilities 52.8 60.5
Recurring    
Assets:    
Total assets 74.2 114.6
Digital assets - safeguarded assets 40.2 22.9
Liabilities:    
Contingent consideration liabilities 28.2 39.1
Digital assets - safeguarded liabilities 40.2 22.9
Cboe Digital restricted common units liability 18.7 15.5
Cboe Digital warrant liability 5.9 5.9
Total liabilities 93.0 83.4
Recurring | U.S. Treasury securities    
Assets:    
Total assets 0.5 64.2
Recurring | Marketable securities | Mutual funds    
Assets:    
Total assets 14.4 15.3
Recurring | Marketable securities | Money market funds    
Assets:    
Total assets 19.1 12.2
Recurring | Level 1    
Assets:    
Total assets 74.2 114.6
Digital assets - safeguarded assets 40.2 22.9
Liabilities:    
Digital assets - safeguarded liabilities 40.2 22.9
Total liabilities 40.2 22.9
Recurring | Level 1 | U.S. Treasury securities    
Assets:    
Total assets 0.5 64.2
Recurring | Level 1 | Marketable securities | Mutual funds    
Assets:    
Total assets 14.4 15.3
Recurring | Level 1 | Marketable securities | Money market funds    
Assets:    
Total assets 19.1 12.2
Recurring | Level 3    
Liabilities:    
Contingent consideration liabilities 28.2 39.1
Cboe Digital restricted common units liability 18.7 15.5
Cboe Digital warrant liability 5.9 5.9
Total liabilities $ 52.8 $ 60.5