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Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - Schedule of Gross Derivative Assets and Liabilities by Type and Balance Sheet Location (Details)
contract in Millions, $ in Millions
Jun. 30, 2025
USD ($)
contract
Sep. 30, 2024
USD ($)
contract
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset $ 6,732.4 $ 7,235.9
Derivative liability, fair value, gross liability 6,629.6 7,144.1
Impact of netting and collateral asset (6,689.8) (6,670.6)
Impact of netting and collateral liability $ (6,659.6) $ (6,614.6)
Derivative, number of instruments held | contract 12.7 12.2
Total fair value included in Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net    
Derivatives, Fair Value [Line Items]    
Derivative, fair value, net $ (160.8) $ 336.0
Total fair value included in Receivable from clients, net    
Derivatives, Fair Value [Line Items]    
Derivative, fair value, net 18.2 (8.4)
Total fair value included in Financial instruments owned, at fair value    
Derivatives, Fair Value [Line Items]    
Derivative, fair value, net 185.2 237.7
Total fair value included in Payables to clients    
Derivatives, Fair Value [Line Items]    
Derivative, fair value, net (103.5) 265.9
Total fair value included in Payables to broker-dealers, clearing organizations and counterparties    
Derivatives, Fair Value [Line Items]    
Derivative, fair value, net (134.2) (1.4)
Total fair value included in Financial instruments sold, not yet purchased, at fair value    
Derivatives, Fair Value [Line Items]    
Derivative, fair value, net 207.7 265.0
Not Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 6,715.1 7,226.3
Derivative liability, fair value, gross liability 6,629.6 7,143.9
Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 17.3 9.6
Derivative liability, fair value, gross liability 0.0 0.2
Exchange-traded commodity derivatives | Not Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 1,834.2 1,383.1
Derivative liability, fair value, gross liability 1,876.6 1,415.7
OTC commodity derivatives | Not Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 2,702.0 1,967.9
Derivative liability, fair value, gross liability 2,576.3 1,924.3
Exchange-traded foreign exchange derivatives | Not Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 7.9 2.0
Derivative liability, fair value, gross liability 7.9 2.0
OTC foreign exchange derivatives | Not Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 813.4 975.2
Derivative liability, fair value, gross liability 821.8 938.2
Exchange-traded interest rate derivatives | Not Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 509.2 720.1
Derivative liability, fair value, gross liability 513.7 728.1
OTC interest rate derivatives | Not Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 161.6 207.1
Derivative liability, fair value, gross liability 161.6 207.1
OTC interest rate derivatives | Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 0.0 0.0
Derivative liability, fair value, gross liability 0.0 0.2
Exchange-traded equity index derivatives | Not Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 412.4 1,817.4
Derivative liability, fair value, gross liability 412.4 1,817.4
OTC equity and indices derivatives | Not Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 212.9 127.4
Derivative liability, fair value, gross liability 141.0 86.7
TBA and forward settling securities | Not Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 61.5 26.1
Derivative liability, fair value, gross liability 118.3 24.4
Foreign currency forward contracts | Designated as Hedging Instrument    
Derivatives, Fair Value [Line Items]    
Derivative asset, fair value, gross asset 17.3 9.6
Derivative liability, fair value, gross liability $ 0.0 $ 0.0