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Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
Jun. 30, 2024
Jun. 30, 2023
Jun. 30, 2024
Jun. 30, 2023
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer $ 571.8 $ 980.7 $ 1,708.4 $ 2,844.9
Principal gains, net 305.6 300.0 881.2 810.8
Interest income 379.6 262.7 995.7 685.7
Total revenues 27,069.7 15,047.9 68,748.8 44,220.5
Total operating revenues 913.7 776.9 2,516.1 2,136.1
United States        
Disaggregation of Revenue [Line Items]        
Total revenues 1,400.2 1,428.9 4,411.4 4,463.6
Total operating revenues 657.9 559.6 1,815.9 1,588.0
Europe        
Disaggregation of Revenue [Line Items]        
Total revenues 618.9 1,014.8 1,837.5 2,841.8
Total operating revenues 162.5 145.1 459.2 352.1
South America        
Disaggregation of Revenue [Line Items]        
Total revenues 118.5 65.9 351.5 184.6
Total operating revenues 43.5 34.3 109.9 97.8
Middle East and Asia        
Disaggregation of Revenue [Line Items]        
Total revenues 24,923.7 12,534.9 62,124.4 36,721.2
Total operating revenues 41.4 34.4 107.1 88.9
Other        
Disaggregation of Revenue [Line Items]        
Total revenues 8.4 3.4 24.0 9.3
Total operating revenues 8.4 3.5 24.0 9.3
Point-in-time        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 528.3 941.9 1,587.7 2,729.2
Time elapsed        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 43.5 38.8 120.7 115.7
Exchange-traded futures and options        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 59.4 57.6 166.6 161.6
OTC derivative brokerage        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 2.8 2.0 8.6 10.1
Equities and fixed income        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 17.8 13.6 48.8 44.6
Mutual funds        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 0.8 0.7 2.4 2.2
Insurance and annuity products        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 2.4 2.0 8.1 6.5
Other        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 0.0 2.0 0.1 4.2
Total sales-based commission        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 83.2 77.9 234.6 229.2
Mutual funds        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 3.2 3.1 9.4 9.2
Insurance and annuity products        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 3.9 3.5 11.3 10.5
Total trailing commission        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 7.1 6.6 20.7 19.7
Clearing fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 47.2 38.6 135.9 114.6
Trade conversion fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 3.3 1.7 10.8 6.1
Other        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 2.2 2.0 6.9 5.9
Total commission and clearing fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 143.0 126.8 408.9 375.5
Total revenues 143.0 126.8 408.9 375.5
Underwriting fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 0.1 0.2 0.2 0.5
Asset management fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 13.3 11.5 37.0 33.3
Advisory and consulting fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 12.4 8.4 29.6 26.1
Sweep program fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 10.7 12.3 33.4 36.6
Client account fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 4.6 4.0 13.1 11.5
Other        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 4.2 2.8 10.7 11.7
Total consulting, management, and account fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 45.3 39.2 124.0 119.7
Total revenues 45.3 39.2 124.0 119.7
Precious metals sales under ASC Topic 606        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 383.5 814.7 1,175.5 2,349.7
Physical precious metals under ASC Topic 815        
Disaggregation of Revenue [Line Items]        
Sales of physical commodities 25,030.2 12,513.4 62,259.7 36,695.5
Physical agricultural and energy products        
Disaggregation of Revenue [Line Items]        
Sales of physical commodities $ 782.5 $ 991.1 $ 2,903.8 $ 3,183.6
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 2.10% 6.50% 2.50% 6.40%