Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 850.6	$ 616.3	$ 2,742.1	$ 1,434.9
Principal gains, net	295.2	232.1	869.8	700.7
Interest income	50.1	27.8	112.3	72.4
Revenues	18,930.9	10,192.1	49,655.0	30,687.4
Total operating revenues	528.8	431.5	1,524.0	1,283.0
United States
Disaggregation of Revenue [Line Items]
Revenues	1,278.3	808.2	3,607.6	2,420.7
Total operating revenues	354.7	310.3	1,023.3	946.2
Europe
Disaggregation of Revenue [Line Items]
Revenues	813.1	542.7	2,631.3	1,205.2
Total operating revenues	125.8	77.2	364.8	224.8
South America
Disaggregation of Revenue [Line Items]
Revenues	21.7	20.2	63.0	49.3
Total operating revenues	21.7	19.9	63.0	49.0
Middle East and Asia
Disaggregation of Revenue [Line Items]
Revenues	16,814.7	8,818.7	43,345.4	27,005.8
Total operating revenues	23.5	21.6	65.3	56.4
Other
Disaggregation of Revenue [Line Items]
Revenues	3.1	2.3	7.7	6.4
Total operating revenues	3.1	2.5	7.6	6.6
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	821.1	591.5	2,658.5	1,362.9
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	29.5	24.8	83.6	72.0
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	53.1	51.8	155.4	147.5
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.0	3.8	13.3	12.2
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	15.4	13.2	47.1	47.0
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.0	1.4	3.4	4.1
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.2	2.2	7.4	6.8
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.6	0.9	2.3	1.2
Total sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	76.3	73.3	228.9	218.8
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.4	3.7	10.9	10.6
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.9	4.4	12.5	12.5
Total trailing commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	7.3	8.1	23.4	23.1
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	38.8	37.4	115.8	115.3
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.0	3.2	9.0	8.9
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.5	2.0	4.5	7.1
Total commission and clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	126.9	124.0	381.6	373.2
Underwriting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.1	0.2	0.4	0.6
Asset management fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	11.5	9.8	33.5	27.8
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	8.2	6.3	23.2	18.9
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.5	0.6	3.5	2.2
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.8	3.6	11.8	11.5
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.6	1.8	4.8	6.4
Total consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	27.7	22.3	77.2	67.4
Precious metals sales
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	696.0	470.0	2,283.3	994.3
Physical precious metals trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	16,808.1	8,817.1	43,334.7	26,997.4
Physical agricultural and energy product trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 926.9	$ 498.8	$ 2,596.1	$ 1,482.0