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Revenue from Contracts with Clients - Schedule of Revenue from Contracts with Clients (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
Jun. 30, 2025
Jun. 30, 2024
Jun. 30, 2025
Jun. 30, 2024
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer $ 851.2 $ 571.8 $ 2,334.7 $ 1,708.4
Principal gains, net 334.0 305.6 943.4 881.2
Interest income 442.7 379.6 1,209.9 995.7
Total revenues 34,828.8 27,069.7 99,654.8 68,748.8
Total operating revenues 1,024.3 913.7 2,924.6 2,516.1
United States        
Disaggregation of Revenue [Line Items]        
Total revenues 1,930.5 1,400.2 5,594.9 4,411.4
Total operating revenues 733.1 657.9 2,097.1 1,815.9
Europe        
Disaggregation of Revenue [Line Items]        
Total revenues 900.2 618.9 2,446.2 1,837.5
Total operating revenues 175.4 162.5 484.3 459.2
South America        
Disaggregation of Revenue [Line Items]        
Total revenues 106.5 118.5 411.5 351.5
Total operating revenues 46.2 43.5 131.2 109.9
Middle East and Asia        
Disaggregation of Revenue [Line Items]        
Total revenues 31,877.0 24,923.7 91,191.9 62,124.4
Total operating revenues 55.0 41.4 175.9 107.1
Other        
Disaggregation of Revenue [Line Items]        
Total revenues 14.6 8.4 10.3 24.0
Total operating revenues 14.6 8.4 36.1 24.0
Point-in-time        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 808.4 528.3 2,207.0 1,587.7
Time elapsed        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 42.8 43.5 127.7 120.7
Exchange-traded futures and options        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 72.8 59.4 207.0 166.6
OTC derivative brokerage        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 2.9 2.8 8.2 8.6
Equities and fixed income        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 16.5 17.8 46.6 48.8
Mutual funds        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 0.7 0.8 2.3 2.4
Insurance and annuity products        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 2.8 2.4 9.3 8.1
Other        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 0.3 0.0 1.1 0.1
Total sales-based commission        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 96.0 83.2 274.5 234.6
Mutual funds        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 3.3 3.2 10.2 9.4
Insurance and annuity products        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 3.9 3.9 11.9 11.3
Total trailing commission        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 7.2 7.1 22.1 20.7
Clearing fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 49.1 47.2 141.2 135.9
Trade conversion fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 2.5 3.3 8.1 10.8
Other        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 11.2 2.2 33.7 6.9
Total commission and clearing fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 166.0 143.0 479.6 408.9
Total revenues 166.0 143.0 479.6 408.9
Underwriting fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 0.3 0.1 0.8 0.2
Asset management fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 17.1 13.3 46.3 37.0
Advisory and consulting fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 7.8 12.4 25.6 29.6
Sweep program fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 10.7 10.7 33.7 33.4
Client account fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 7.4 4.6 20.1 13.1
Other        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 2.9 4.2 11.8 10.7
Total consulting, management, and account fees        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 46.2 45.3 138.3 124.0
Total revenues 46.2 45.3 138.3 124.0
Precious metals sales under ASC Topic 606        
Disaggregation of Revenue [Line Items]        
Revenue from contract with customer 639.0 383.5 1,716.8 1,175.5
Physical precious metals under ASC Topic 815        
Disaggregation of Revenue [Line Items]        
Sales of physical commodities 32,102.3 25,030.2 91,857.9 62,259.7
Physical agricultural and energy products        
Disaggregation of Revenue [Line Items]        
Sales of physical commodities $ 1,098.6 $ 782.5 $ 3,308.9 $ 2,903.8
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 2.40% 2.10% 2.30% 2.50%