Acquisitions - Gain Capital Holdings Inc (Details) - USD ($) $ / shares in Units, $ in Millions	1 Months Ended	12 Months Ended
	Feb. 29, 2020	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Aggregated Merger Consideration
Common stock outstanding (in shares)		20,303,904	19,823,910
Total revenues		$ 66,036.0	$ 42,534.2	$ 54,139.6
Gain Capital Holdings Inc
Aggregated Merger Consideration
Common stock outstanding (in shares)	3,600,000
Gain Capital Holdings Inc
Business Acquisition [Line Items]
Business acquisition, share price (in dollars per share)	$ 6.00
Aggregated Merger Consideration
Aggregate cash consideration	$ 215.0
Accrual for merger cash consideration	21.6
Total merger consideration	$ 236.6		$ 236.6
Total revenues				49.0
Net income				1.8
Business acquisition, cost incurred related to merger				$ 5.2