Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2021	Mar. 31, 2020	Mar. 31, 2021	Mar. 31, 2020
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 151.9	$ 139.2	$ 294.3	$ 247.7
Principal gains, net	265.2	168.5	468.6	281.0
Interest income	23.4	41.7	44.6	87.7
Total revenues	11,244.8	20,366.3	20,495.3	31,611.3
United States
Disaggregation of Revenue [Line Items]
Total revenues	853.6	585.6	1,612.5	1,097.9
Europe
Disaggregation of Revenue [Line Items]
Total revenues	490.1	150.0	662.5	261.6
South America
Disaggregation of Revenue [Line Items]
Total revenues	14.5	16.3	29.1	31.5
Middle East and Asia
Disaggregation of Revenue [Line Items]
Total revenues	9,885.1	19,613.3	18,187.1	30,218.8
Other
Disaggregation of Revenue [Line Items]
Total revenues	1.5	1.1	4.1	1.5
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	127.4	113.7	247.1	198.3
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	24.5	25.5	47.2	49.4
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	49.4	40.1	95.7	72.5
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.6	6.7	8.4	12.2
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	19.4	7.1	33.8	11.4
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.5	1.6	2.7	2.9
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.3	2.4	4.6	4.5
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.1	0.5	0.3	0.8
Sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	77.3	58.4	145.5	104.3
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.6	3.5	6.9	6.6
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.2	4.0	8.1	7.7
Trailing commissions
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	7.8	7.5	15.0	14.3
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	39.4	41.6	77.9	71.1
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.6	4.2	5.7	5.7
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.7	4.9	5.1	8.4
Commission and clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	129.8	116.6	249.2	203.8
Underwriting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.2	0.2	0.4	0.4
Asset management fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	9.3	8.7	18.0	16.2
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	6.6	5.7	12.6	11.3
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.8	3.6	1.6	7.6
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.8	3.1	7.9	6.1
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.4	1.3	4.6	2.3
Consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	22.1	22.6	45.1	43.9
Physical precious metals trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	10,295.7	19,694.7	18,704.6	30,352.7
Physical agricultural and energy product trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 508.6	$ 322.2	$ 983.2	$ 642.2