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Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - Schedule of Derivative Assets and Liabilities (Details) contract in Millions, $ in Millions | Dec. 31, 2024 USD ($) contract | Sep. 30, 2024 USD ($) contract
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Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | $ 7,883.5 | $ 7,235.9
Derivative liability, fair value, gross liability | 7,724.8 | 7,144.1
Impact of netting and collateral asset | (7,136.0) | (6,670.6)
Impact of netting and collateral liability | $ (7,026.4) | $ (6,614.6)
Derivative, number of instruments held | contract | 11.3 | 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 | $ 523.1 | $ 336.0
Total fair value included in Receivable from clients, net |  |
Derivatives, Fair Value [Line Items] |  |
Derivative, fair value, net | (2.8) | (8.4)
Total fair value included in Financial instruments owned, at fair value |  |
Derivatives, Fair Value [Line Items] |  |
Derivative, fair value, net | 227.2 | 237.7
Total fair value included in Payables to clients |  |
Derivatives, Fair Value [Line Items] |  |
Derivative, fair value, net | 371.1 | 265.9
Total fair value included in Payables to broker-dealers, clearing organizations and counterparties |  |
Derivatives, Fair Value [Line Items] |  |
Derivative, fair value, net | 37.5 | (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 | 289.8 | 265.0
Not Designated as Hedging Instrument |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 7,882.3 | 7,226.3
Derivative liability, fair value, gross liability | 7,723.9 | 7,143.9
Designated as Hedging Instrument |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 1.2 | 9.6
Derivative liability, fair value, gross liability | 0.9 | 0.2
Exchange-traded commodity derivatives | Not Designated as Hedging Instrument |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 1,303.8 | 1,383.1
Derivative liability, fair value, gross liability | 1,281.3 | 1,415.7
OTC commodity derivatives | Not Designated as Hedging Instrument |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 2,919.4 | 1,967.9
Derivative liability, fair value, gross liability | 2,817.1 | 1,924.3
Exchange-traded foreign exchange derivatives | Not Designated as Hedging Instrument |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | (1.7) | 2.0
Derivative liability, fair value, gross liability | 2.1 | 2.0
OTC foreign exchange derivatives | Not Designated as Hedging Instrument |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 815.1 | 975.2
Derivative liability, fair value, gross liability | 858.2 | 938.2
Exchange-traded interest rate derivatives | Not Designated as Hedging Instrument |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 587.8 | 720.1
Derivative liability, fair value, gross liability | 590.9 | 728.1
OTC interest rate derivatives | Not Designated as Hedging Instrument |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 220.4 | 207.1
Derivative liability, fair value, gross liability | 220.4 | 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 | 1,810.0 | 1,817.4
Derivative liability, fair value, gross liability | 1,810.0 | 1,817.4
OTC equity and indices derivatives | Not Designated as Hedging Instrument |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 153.5 | 127.4
Derivative liability, fair value, gross liability | 113.0 | 86.7
TBA and forward settling securities | Not Designated as Hedging Instrument |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 74.0 | 26.1
Derivative liability, fair value, gross liability | 30.9 | 24.4
Foreign currency forward contracts | Designated as Hedging Instrument |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 1.2 | 9.6
Derivative liability, fair value, gross liability | $ 0.9 | $ 0.0

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