Acquisitions - Gain Capital Holdings Inc Post Acquisition Results and Unaudited Pro Forma Information (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Business Acquisition [Line Items]
Total revenues	$ 42,534.2	$ 54,139.6	$ 32,897.0
Gain Capital Holdings Inc
Business Acquisition [Line Items]
Total revenues		49.0
Net income		1.8
Business Acquisition, Pro Forma Information [Abstract]
Total revenues		54,414.1	33,160.0
Net income		$ 138.5	$ 38.3
Basic earnings per share (in dollars per share)		$ 7.17	$ 2.01
Diluted earnings per share (in dollars per share)		$ 7.02	$ 1.97