Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Jun. 30, 2023	Jun. 30, 2022	Jun. 30, 2023	Jun. 30, 2022
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 980.7	$ 850.6	$ 2,844.9	$ 2,742.1
Principal gains, net	300.0	295.2	810.8	869.8
Interest income	262.7	50.1	685.7	112.3
Revenues	15,047.9	18,930.9	44,220.5	49,655.0
Total operating revenues	776.9	528.8	2,136.1	1,524.0
United States
Disaggregation of Revenue [Line Items]
Revenues	1,428.9	1,278.3	4,463.6	3,607.6
Total operating revenues	559.6	354.7	1,588.0	1,023.3
Europe
Disaggregation of Revenue [Line Items]
Revenues	1,014.8	813.1	2,841.8	2,631.3
Total operating revenues	145.1	125.8	352.1	364.8
South America
Disaggregation of Revenue [Line Items]
Revenues	65.9	21.7	184.6	63.0
Total operating revenues	34.3	21.7	97.8	63.0
Middle East and Asia
Disaggregation of Revenue [Line Items]
Revenues	12,534.9	16,814.7	36,721.2	43,345.4
Total operating revenues	34.4	23.5	88.9	65.3
Other
Disaggregation of Revenue [Line Items]
Revenues	3.4	3.1	9.3	7.7
Total operating revenues	3.5	3.1	9.3	7.6
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	941.9	821.1	2,729.2	2,658.5
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	38.8	29.5	115.7	83.6
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	57.6	53.1	161.6	155.4
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.0	4.0	10.1	13.3
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	13.6	15.4	44.6	47.1
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.7	1.0	2.2	3.4
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.0	2.2	6.5	7.4
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.0	0.6	4.2	2.3
Total sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	77.9	76.3	229.2	228.9
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.1	3.4	9.2	10.9
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.5	3.9	10.5	12.5
Total trailing commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	6.6	7.3	19.7	23.4
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	38.6	38.8	114.6	115.8
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.7	3.0	6.1	9.0
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.0	1.5	5.9	4.5
Total commission and clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	126.8	126.9	375.5	381.6
Revenues	126.8	126.9	375.5	381.6
Underwriting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.2	0.1	0.5	0.4
Asset management fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	11.5	11.5	33.3	33.5
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	8.4	8.2	26.1	23.2
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	12.3	2.5	36.6	3.5
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.0	3.8	11.5	11.8
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.8	1.6	11.7	4.8
Total consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	39.2	27.7	119.7	77.2
Revenues	39.2	27.7	119.7	77.2
Precious metals sales
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	814.7	696.0	2,349.7	2,283.3
Physical precious metals trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	12,513.4	16,808.1	36,695.5	43,334.7
Physical agricultural and energy product trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 991.1	$ 926.9	$ 3,183.6	$ 2,596.1
Revenue from Contract with Customer Benchmark | Customer Concentration Risk | Clients
Disaggregation of Revenue [Line Items]
Revenues from contracts with clients as a percentage of total revenues	6.50%	4.50%	6.40%	5.50%