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Revenue from Contracts with Clients - Schedule of Revenue from Contracts with Clients (Details) - USD ($) $ in Millions | 3 Months Ended
--- | ---
Dec. 31, 2024 | Dec. 31, 2023
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | $ 663.1 | $ 627.4
Principal gains, net | 308.9 | 293.8
Interest income | 378.2 | 290.1
Total revenues | 27,935.3 | 19,573.0
Total operating revenues | 944.3 | 784.2
United States |  |
Disaggregation of Revenue [Line Items] |  |
Total revenues | 1,695.6 | 1,603.5
Total operating revenues | 659.1 | 568.0
Europe |  |
Disaggregation of Revenue [Line Items] |  |
Total revenues | 782.5 | 658.4
Total operating revenues | 189.6 | 135.6
South America |  |
Disaggregation of Revenue [Line Items] |  |
Total revenues | 168.0 | 128.0
Total operating revenues | 35.9 | 41.2
Middle East and Asia |  |
Disaggregation of Revenue [Line Items] |  |
Total revenues | 25,285.4 | 17,175.6
Total operating revenues | 55.9 | 32.0
Other |  |
Disaggregation of Revenue [Line Items] |  |
Total revenues | 3.8 | 7.5
Total operating revenues | 3.8 | 7.4
Point-in-time |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 620.7 | 589.7
Time elapsed |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 42.4 | 37.7
Exchange-traded futures and options |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 63.2 | 51.4
OTC derivative brokerage |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 2.8 | 2.8
Equities and fixed income |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 15.1 | 16.5
Mutual funds |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 0.8 | 0.7
Insurance and annuity products |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 3.2 | 2.0
Other |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 0.4 | (0.1)
Total sales-based commission |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 85.5 | 73.3
Mutual funds |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 3.4 | 3.0
Insurance and annuity products |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 4.0 | 3.7
Total trailing commission |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 7.4 | 6.7
Clearing fees |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 44.1 | 43.3
Trade conversion fees |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 2.2 | 4.0
Other |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 10.1 | 2.4
Total commission and clearing fees |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 149.3 | 129.7
Total revenues | 149.3 | 129.7
Underwriting fees |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 0.3 | 0.0
Asset management fees |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 14.8 | 11.4
Advisory and consulting fees |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 8.6 | 8.2
Sweep program fees |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 11.6 | 11.4
Client account fees |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 6.2 | 4.2
Other |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 6.3 | 3.3
Total consulting, management, and account fees |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 47.8 | 38.5
Total revenues | 47.8 | 38.5
Precious metals sales under ASC Topic 606 |  |
Disaggregation of Revenue [Line Items] |  |
Revenue from contract with customer | 466.0 | 459.2
Physical precious metals under ASC Topic 815 |  |
Disaggregation of Revenue [Line Items] |  |
Sales of physical commodities | 25,522.4 | 17,162.5
Physical agricultural and energy products |  |
Disaggregation of Revenue [Line Items] |  |
Sales of physical commodities | $ 1,062.7 | $ 1,199.2
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% | 3.20%

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