Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Mar. 31, 2023	Mar. 31, 2024	Mar. 31, 2023
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 509.2	$ 917.8	$ 1,136.6	$ 1,864.2
Principal gains, net	281.8	256.6	575.6	510.8
Interest income	326.0	226.8	616.1	423.0
Total revenues	22,106.1	16,161.0	41,679.1	29,172.6
Total operating revenues	818.2	704.4	1,602.4	1,359.2
United States
Disaggregation of Revenue [Line Items]
Total revenues	1,407.7	1,471.1	3,011.2	3,034.7
Total operating revenues	590.0	538.5	1,158.0	1,028.4
Europe
Disaggregation of Revenue [Line Items]
Total revenues	560.2	912.0	1,218.6	1,827.0
Total operating revenues	161.1	105.5	296.7	207.0
South America
Disaggregation of Revenue [Line Items]
Total revenues	105.0	56.5	233.0	118.7
Total operating revenues	25.2	32.0	66.4	63.5
Middle East and Asia
Disaggregation of Revenue [Line Items]
Total revenues	20,025.1	13,720.0	37,200.7	24,186.3
Total operating revenues	33.7	27.1	65.7	54.5
Other
Disaggregation of Revenue [Line Items]
Total revenues	8.1	1.4	15.6	5.9
Total operating revenues	8.2	1.3	15.6	5.8
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	469.7	878.2	1,059.4	1,787.3
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	39.5	39.6	77.2	76.9
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	55.8	55.3	107.2	104.0
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.0	4.5	5.8	8.1
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	14.5	15.6	31.0	31.0
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.9	0.9	1.6	1.5
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.7	2.7	5.7	4.5
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.2	1.1	0.1	2.2
Total sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	78.1	80.1	151.4	151.3
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.2	3.1	6.2	6.1
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.7	3.5	7.4	7.0
Total trailing commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	6.9	6.6	13.6	13.1
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	45.4	40.0	88.7	76.0
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.5	2.0	7.5	4.4
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.3	2.0	4.7	3.9
Total commission and clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	136.2	130.7	265.9	248.7
Total revenues	136.2	130.7	265.9	248.7
Underwriting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.1	0.1	0.1	0.3
Asset management fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	12.3	11.1	23.7	21.8
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	9.0	9.0	17.2	17.7
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	11.3	12.9	22.7	24.3
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.3	3.7	8.5	7.5
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.2	3.9	6.5	8.9
Total consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	40.2	40.7	78.7	80.5
Total revenues	40.2	40.7	78.7	80.5
Precious metals sales under ASC Topic 606
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	332.8	746.4	792.0	1,535.0
Physical precious metals under ASC Topic 815
Disaggregation of Revenue [Line Items]
Sales of physical commodities	20,067.0	13,703.1	37,229.5	24,182.1
Physical agricultural and energy products
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 922.1	$ 1,056.7	$ 2,121.3	$ 2,192.5
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	2.30%	5.70%	2.70%	6.40%