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	Dec. 31, 2023 USD ($) contract	Sep. 30, 2023 USD ($) contract
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	$ 7,386.6	$ 8,200.3
Derivative liability, fair value, gross liability	7,227.7	8,017.3
Impact of netting and collateral asset	(6,636.9)	(7,731.3)
Impact of netting and collateral liability	$ (6,477.7)	$ (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	$ 505.2	$ 206.7
Total fair value included in Receivable from clients, net
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	1.1	(7.9)
Total fair value included in Financial instruments owned, at fair value
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	243.4	270.2
Total fair value included in Payables to clients
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	453.0	79.8
Total fair value included in Payables to broker-dealers, clearing organizations and counterparties
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	51.5	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	245.5	288.3
Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	7,376.4	8,198.6
Derivative liability, fair value, gross liability	7,219.7	7,990.2
Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	10.2	1.7
Derivative liability, fair value, gross liability	8.0	27.1
Exchange-traded commodity derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1,381.9	1,907.0
Derivative liability, fair value, gross liability	1,367.1	1,890.3
OTC commodity derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1,738.8	1,523.3
Derivative liability, fair value, gross liability	1,665.0	1,456.0
Exchange-traded foreign exchange derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	2.9	4.3
Derivative liability, fair value, gross liability	2.9	4.3
OTC foreign exchange derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	469.8	497.1
Derivative liability, fair value, gross liability	415.4	455.3
Exchange-traded interest rate derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1,228.8	1,507.6
Derivative liability, fair value, gross liability	1,235.3	1,509.8
OTC interest rate derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	247.0	417.6
Derivative liability, fair value, gross liability	247.0	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	8.0	24.6
Exchange-traded equity index derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	2,134.1	2,140.9
Derivative liability, fair value, gross liability	2,134.1	2,140.9
OTC equity and indices derivatives | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	146.9	127.3
Derivative liability, fair value, gross liability	81.6	68.5
TBA and forward settling securities | Not Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	26.2	73.5
Derivative liability, fair value, gross liability	71.3	47.5
Foreign currency forward contracts | Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	10.2	1.7
Derivative liability, fair value, gross liability	$ 0.0	$ 2.5