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Revenue from Contracts with Clients - Schedule of Disaggregation of Revenue (Details) - USD ($) $ in Millions | 12 Months Ended
--- | ---
Sep. 30, 2025 | Sep. 30, 2024 | Sep. 30, 2023
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | $ 3,067.6 | $ 2,215.9 | $ 3,493.4
Principal gains, net | 1,247.2 | 1,189.6 | 1,079.9
Interest income | 1,734.3 | 1,396.8 | 987.6
Total revenues | 132,378.2 | 99,887.8 | 60,856.1
Point-in-time |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 2,896.3 | 2,054.5 | 3,338.1
Time elapsed |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 171.3 | 161.4 | 155.3
Total commission and clearing fees |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 728.2 | 548.0 | 498.4
Total revenues | 728.2 | 548.0 | 498.4
Total sales-based commission |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 478.1 | 317.4 | 302.0
Exchange-traded futures and options |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 341.0 | 226.1 | 214.1
OTC derivative brokerage |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 11.0 | 11.3 | 14.5
Equities and fixed income |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 109.1 | 65.9 | 57.8
Mutual funds |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 3.3 | 3.1 | 3.0
Insurance and annuity products |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 12.2 | 11.0 | 9.2
Other |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 1.5 | 0.0 | 3.4
Total trailing commission |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 29.5 | 27.9 | 26.6
Mutual funds |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 13.6 | 12.7 | 12.4
Insurance and annuity products |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 15.9 | 15.2 | 14.2
Clearing fees |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 207.0 | 180.2 | 153.3
Trade conversion fees |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 10.5 | 13.1 | 8.5
Other |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 3.1 | 9.4 | 8.0
Total consulting, management, and account fees |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 205.9 | 167.2 | 159.0
Total revenues | 205.9 | 167.2 | 159.0
Underwriting fees |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 8.6 | 0.4 | 0.7
Asset management fees |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 62.7 | 50.9 | 45.1
Advisory and consulting fees |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 34.3 | 38.2 | 35.0
Sweep program fees |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 44.8 | 44.4 | 48.6
Client account fees |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 36.9 | 19.8 | 15.9
Other |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 18.6 | 13.5 | 13.7
Precious metals sales under ASC Topic 606 |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue from contract with customer | 2,133.5 | 1,500.7 | 2,836.0
Physical precious metals under ASC Topic 815 |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Sales of physical commodities | 121,824.0 | 91,241.1 | 50,979.5
Physical agricultural and energy products |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Sales of physical commodities | $ 4,505.1 | $ 3,844.4 | $ 4,315.7

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