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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	Sep. 30, 2024 USD ($) contract	Sep. 30, 2023 USD ($) contract
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	$ 7,235.9	$ 8,200.3
Derivative liability, fair value, gross liability	7,144.1	8,017.3
Impact of netting and collateral asset	(6,670.6)	(7,731.3)
Impact of netting and collateral liability	$ (6,614.6)	$ (7,639.0)
Derivative, number of instruments held | contract	12.2	13.4
Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	$ 7,226.3	$ 8,198.6
Derivative liability, fair value, gross liability	7,143.9	7,990.2
Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	9.6	1.7
Derivative liability, fair value, gross liability	0.2	27.1
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	336.0	206.7
Total fair value included in Receivable from clients, net
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	(8.4)	(7.9)
Total fair value included in Financial instruments owned, at fair value
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	237.7	270.2
Total fair value included in Payables to clients
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	265.9	79.8
Total fair value included in Payables to broker-dealers, clearing organizations and counterparties
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	(1.4)	10.2
Fair value included in Financial instruments sold, not yet purchased, at fair value
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	265.0	288.3
Exchange-traded commodity derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1,383.1	1,907.0
Derivative liability, fair value, gross liability	1,415.7	1,890.3
OTC commodity derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1,967.9	1,523.3
Derivative liability, fair value, gross liability	1,924.3	1,456.0
Exchange-traded foreign exchange derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	2.0	4.3
Derivative liability, fair value, gross liability	2.0	4.3
OTC foreign exchange derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	975.2	497.1
Derivative liability, fair value, gross liability	938.2	455.3
Exchange-traded interest rate derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	720.1	1,507.6
Derivative liability, fair value, gross liability	728.1	1,509.8
OTC interest rate derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	207.1	417.6
Derivative liability, fair value, gross liability	207.1	417.6
OTC interest rate derivatives | Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative liability, fair value, gross liability	0.2	24.6
Exchange-traded equity index derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1,817.4	2,140.9
Derivative liability, fair value, gross liability	1,817.4	2,140.9
OTC equity and indices derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	127.4	127.3
Derivative liability, fair value, gross liability	86.7	68.5
TBA and forward settling securities | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	26.1	73.5
Derivative liability, fair value, gross liability	24.4	47.5
Interest rate swaps | 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	0.2	24.6
Foreign currency forwards | Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	9.6	1.7
Derivative liability, fair value, gross liability	$ 0.0	$ 2.5

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Fair value of liability associated with financial asset or other contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset, and obligation to return cash collateral under master netting arrangements.

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