FAIR VALUE MEASUREMENT - Fair value hierarchy for assets and liabilities on a recurring basis (Details) - USD ($) $ in Millions	Sep. 30, 2024	Dec. 31, 2023
Assets:
Note receivable - building sale	$ 6.4
Digital assets - safeguarded assets	0.0	$ 51.3
Total assets	45.8	108.9
Liabilities:
Contingent consideration liabilities		11.8
Digital assets - safeguarded liabilities	0.0	51.3
Cboe Digital restricted common units liability		18.7
Cboe Digital warrant liability		5.9
Total liabilities	1,385.5	1,430.1
Level 1
Assets:
Note receivable - building sale	0.0
Digital assets - safeguarded assets		0.0
Total assets	39.4	57.6
Liabilities:
Contingent consideration liabilities		0.0
Digital assets - safeguarded liabilities		0.0
Cboe Digital restricted common units liability		0.0
Cboe Digital warrant liability		0.0
Total liabilities	38.9	36.7
Level 2
Assets:
Note receivable - building sale	0.0
Digital assets - safeguarded assets		51.3
Total assets	0.0	51.3
Liabilities:
Contingent consideration liabilities		0.0
Digital assets - safeguarded liabilities		51.3
Cboe Digital restricted common units liability		0.0
Cboe Digital warrant liability		0.0
Total liabilities	1,346.6	1,357.0
Level 3
Assets:
Note receivable - building sale	6.4
Digital assets - safeguarded assets		0.0
Total assets	6.4	0.0
Liabilities:
Contingent consideration liabilities		11.8
Digital assets - safeguarded liabilities		0.0
Cboe Digital restricted common units liability		18.7
Cboe Digital warrant liability		5.9
Total liabilities	0.0	36.4
Fair Value, Recurring
Assets:
Note receivable - building sale	6.4
Digital assets - safeguarded assets		51.3
Total assets	45.8	108.8
Liabilities:
Contingent consideration liabilities		11.8
Digital assets - safeguarded liabilities		51.3
Cboe Digital restricted common units liability		18.7
Cboe Digital warrant liability		5.9
Total liabilities		87.7
Fair Value, Recurring | US Treasury Securities
Assets:
Debt securities	0.5	20.8
Fair Value, Recurring | Mutual funds
Assets:
Marketable securities	21.3	17.1
Fair Value, Recurring | Money market funds
Assets:
Marketable securities	17.6	19.6
Fair Value, Recurring | Level 1
Assets:
Note receivable - building sale	0.0
Digital assets - safeguarded assets		0.0
Total assets	39.4	57.5
Liabilities:
Contingent consideration liabilities		0.0
Digital assets - safeguarded liabilities		0.0
Cboe Digital restricted common units liability		0.0
Cboe Digital warrant liability		0.0
Total liabilities		0.0
Fair Value, Recurring | Level 1 | US Treasury Securities
Assets:
Debt securities	0.5	20.8
Fair Value, Recurring | Level 1 | Mutual funds
Assets:
Marketable securities	21.3	17.1
Fair Value, Recurring | Level 1 | Money market funds
Assets:
Marketable securities	17.6	19.6
Fair Value, Recurring | Level 2
Assets:
Note receivable - building sale	0.0
Digital assets - safeguarded assets		51.3
Total assets	0.0	51.3
Liabilities:
Contingent consideration liabilities		0.0
Digital assets - safeguarded liabilities		51.3
Cboe Digital restricted common units liability		0.0
Cboe Digital warrant liability		0.0
Total liabilities		51.3
Fair Value, Recurring | Level 2 | US Treasury Securities
Assets:
Debt securities	0.0	0.0
Fair Value, Recurring | Level 2 | Mutual funds
Assets:
Marketable securities	0.0	0.0
Fair Value, Recurring | Level 2 | Money market funds
Assets:
Marketable securities	0.0	0.0
Fair Value, Recurring | Level 3
Assets:
Note receivable - building sale	6.4
Digital assets - safeguarded assets		0.0
Total assets	6.4	0.0
Liabilities:
Contingent consideration liabilities		11.8
Digital assets - safeguarded liabilities		0.0
Cboe Digital restricted common units liability		18.7
Cboe Digital warrant liability		5.9
Total liabilities		36.4
Fair Value, Recurring | Level 3 | US Treasury Securities
Assets:
Debt securities	0.0	0.0
Fair Value, Recurring | Level 3 | Mutual funds
Assets:
Marketable securities	0.0	0.0
Fair Value, Recurring | Level 3 | Money market funds
Assets:
Marketable securities	$ 0.0	$ 0.0