Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2021	Dec. 31, 2020
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 920.7	$ 255.5
Sales of physical commodities	13,918.9	8,883.5
Principal gains, net	251.1	203.4
Interest income	31.0	21.2
Total revenues	14,341.4	9,250.5
Total operating revenues	450.5	380.1
United States
Disaggregation of Revenue [Line Items]
Total revenues	1,124.7	758.9
Total operating revenues	304.1	286.2
Europe
Disaggregation of Revenue [Line Items]
Total revenues	884.6	172.4
Total operating revenues	107.7	60.5
South America
Disaggregation of Revenue [Line Items]
Total revenues	17.7	14.6
Total operating revenues	17.7	14.6
Middle East and Asia
Disaggregation of Revenue [Line Items]
Total revenues	12,312.2	8,302.0
Total operating revenues	18.8	16.2
Other
Disaggregation of Revenue [Line Items]
Total revenues	2.2	2.6
Total operating revenues	2.2	2.6
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	893.8	232.8
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	26.9	22.7
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	44.6	46.3
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.4	3.8
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	14.6	14.4
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.2	1.2
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.8	2.3
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.8	0.2
Total sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	68.4	68.2
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.9	3.3
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.4	3.9
Total trailing commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	8.3	7.2
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	36.4	38.5
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.0	2.1
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.2	3.4
Total commission and clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	116.3	119.4
Underwriting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.2	0.2
Asset management fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	10.6	8.7
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	7.5	6.0
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.5	0.8
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.7	4.1
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.6	3.2
Total consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	24.1	23.0
Precious metals sales
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	780.3	113.1
Physical precious metals trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	12,315.3	8,295.8
Physical agricultural and energy product trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 823.3	$ 474.6