Segment Analysis - Segment Reporting (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Mar. 31, 2023	Mar. 31, 2024	Mar. 31, 2023	Sep. 30, 2023
Segment Reporting Information [Line Items]
Total revenues	$ 22,106.1	$ 16,161.0	$ 41,679.1	$ 29,172.6
Operating revenues:	818.2	704.4	1,602.4	1,359.2
Net operating revenues (loss):	422.3	399.4	843.9	781.4
Net contribution:	329.0	316.7	665.8	608.3
Segment income:	204.7	179.4	420.8	352.3
Net operating revenue (loss) with Corporate	(12.8)	(21.8)	(28.4)	(32.9)
Overhead costs and expenses	(119.6)	(100.1)	(224.4)	(189.8)
Gain on acquisition	0.0	0.0	0.0	23.5
Income before tax	72.3	57.5	168.0	153.1
Assets	25,651.0		25,651.0		$ 21,938.7
Corporate
Segment Reporting Information [Line Items]
Total revenues	14.4	2.5	23.6	15.3
Operating revenues:	14.4	2.5	23.6	15.3
Net operating revenues (loss):	(12.8)	(21.8)	(28.4)	(32.9)
Assets	1,267.2		1,267.2		812.3
Eliminations
Segment Reporting Information [Line Items]
Total revenues	(11.4)	(9.1)	(23.6)	(18.9)
Operating revenues:	(11.4)	(9.1)	(23.6)	(18.9)
Commercial
Segment Reporting Information [Line Items]
Net contribution:	119.3	140.9	245.7	256.6
Segment income:	85.6	102.9	172.8	185.7
Commercial | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	21,479.1	15,450.7	40,457.1	27,744.2
Operating revenues:	200.5	220.1	398.9	402.5
Net operating revenues (loss):	164.2	185.1	327.6	337.8
Assets	5,154.8		5,154.8		4,676.3
Institutional
Segment Reporting Information [Line Items]
Net contribution:	102.5	89.3	202.7	183.9
Segment income:	61.3	55.8	126.5	117.8
Institutional | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	463.4	362.5	899.1	706.0
Operating revenues:	463.4	362.5	899.1	706.0
Net operating revenues (loss):	149.8	137.9	298.4	281.1
Assets	17,684.1		17,684.1		15,059.3
Retail
Segment Reporting Information [Line Items]
Net contribution:	69.9	48.4	132.5	87.6
Segment income:	33.2	4.8	61.9	0.6
Retail | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	111.3	304.6	213.0	620.8
Operating revenues:	102.0	78.6	194.5	149.1
Net operating revenues (loss):	74.3	50.8	141.3	94.7
Assets	1,111.8		1,111.8		1,014.2
Payments
Segment Reporting Information [Line Items]
Net contribution:	37.3	38.1	84.9	80.2
Segment income:	24.6	15.9	59.6	48.2
Payments | Operating Segments
Segment Reporting Information [Line Items]
Total revenues	49.3	49.8	109.9	105.2
Operating revenues:	49.3	49.8	109.9	105.2
Net operating revenues (loss):	46.8	$ 47.4	105.0	$ 100.7
Assets	$ 433.1		$ 433.1		$ 376.6