Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 146.3	$ 115.5	$ 440.6	$ 363.2
Principal gains, net	232.1	161.0	700.7	442.0
Interest income	27.8	22.4	72.4	110.1
Total revenues	10,192.1	8,243.4	30,687.4	39,854.7
United States
Disaggregation of Revenue [Line Items]
Total revenues	808.2	554.2	2,420.7	1,652.1
Europe
Disaggregation of Revenue [Line Items]
Total revenues	542.7	114.1	1,205.2	375.7
South America
Disaggregation of Revenue [Line Items]
Total revenues	20.2	14.6	49.3	46.1
Middle East and Asia
Disaggregation of Revenue [Line Items]
Total revenues	8,818.7	7,558.5	27,005.8	37,777.3
Other
Disaggregation of Revenue [Line Items]
Total revenues	2.3	2.0	6.4	3.5
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	121.5	95.1	368.6	293.4
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	24.8	20.4	72.0	69.8
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	51.8	36.4	147.5	108.9
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.8	4.0	12.2	16.2
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	13.2	5.2	47.0	16.6
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.4	1.1	4.1	4.0
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.2	1.7	6.8	6.2
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.9	0.3	1.2	1.1
Sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	73.3	48.7	218.8	153.0
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.7	3.1	10.6	9.7
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.4	3.6	12.5	11.3
Total trailing commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	8.1	6.7	23.1	21.0
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	37.4	33.3	115.3	104.4
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.2	1.8	8.9	7.5
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.0	5.6	7.1	14.0
Total commission and clearing fees:
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	124.0	96.1	373.2	299.9
Underwriting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.2	0.0	0.6	0.4
Asset management fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	9.8	7.0	27.8	23.2
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	6.3	5.7	18.9	17.0
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.6	1.0	2.2	8.6
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.6	2.8	11.5	8.9
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.8	2.9	6.4	5.2
Total consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	22.3	19.4	67.4	63.3
Physical precious metals trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	9,287.1	7,621.2	27,991.7	37,973.9
Physical agricultural and energy product trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 498.8	$ 323.3	$ 1,482.0	$ 965.5