Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - Gross Derivative Assets and Liabilities by Type and Balance Sheet Location (Details) contract in Millions, $ in Millions	Mar. 31, 2024 USD ($) contract	Sep. 30, 2023 USD ($) contract
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	$ 7,776.8	$ 8,200.3
Derivative liability, fair value, gross liability	7,635.4	8,017.3
Impact of netting and collateral asset	(6,679.8)	(7,731.3)
Impact of netting and collateral liability	$ (6,628.7)	$ (7,639.0)
Derivative, number of instruments held | contract	11.8	13.4
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	$ 732.8	$ 206.7
Total fair value included in Receivable from clients, net
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	(3.4)	(7.9)
Total fair value included in Financial instruments owned, at fair value
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	367.6	270.2
Total fair value included in Payables to clients
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	585.6	79.8
Total fair value included in Payables to broker-dealers, clearing organizations and counterparties
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	(21.3)	10.2
Total fair value included in Financial instruments sold, not yet purchased, at fair value
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	442.4	288.3
Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	7,769.7	8,198.6
Derivative liability, fair value, gross liability	7,629.7	7,990.2
Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	7.1	1.7
Derivative liability, fair value, gross liability	5.7	27.1
Exchange-traded commodity derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1,732.5	1,907.0
Derivative liability, fair value, gross liability	1,725.8	1,890.3
OTC commodity derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	2,319.0	1,523.3
Derivative liability, fair value, gross liability	2,269.6	1,456.0
Exchange-traded foreign exchange derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1.4	4.3
Derivative liability, fair value, gross liability	1.4	4.3
OTC foreign exchange derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	326.1	497.1
Derivative liability, fair value, gross liability	280.4	455.3
Exchange-traded interest rate derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	782.2	1,507.6
Derivative liability, fair value, gross liability	791.5	1,509.8
OTC interest rate derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	270.2	417.6
Derivative liability, fair value, gross liability	270.2	417.6
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	5.7	24.6
Exchange-traded equity index derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	2,141.3	2,140.9
Derivative liability, fair value, gross liability	2,141.3	2,140.9
OTC equity and indices derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	171.7	127.3
Derivative liability, fair value, gross liability	126.6	68.5
TBA and forward settling securities | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	25.3	73.5
Derivative liability, fair value, gross liability	22.9	47.5
Foreign currency forward contracts | Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	7.1	1.7
Derivative liability, fair value, gross liability	$ 0.0	$ 2.5