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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