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	Sep. 30, 2023 USD ($) contract	Sep. 30, 2022 USD ($) contract
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	$ 8,200.3	$ 9,657.2
Derivative liability, fair value, gross liability	8,017.3	9,552.4
Impact of netting and collateral asset	(7,731.3)	(10,920.8)
Impact of netting and collateral liability	$ (7,639.0)	$ (10,505.0)
Derivative, number of instruments held | contract	13.4	13.3
Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	$ 8,198.6	$ 9,657.2
Derivative liability, fair value, gross liability	7,990.2	9,481.8
Designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1.7	0.0
Derivative liability, fair value, gross liability	27.1	70.6
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	206.7	(1,455.7)
Total fair value included in Receivable from clients, net
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	(7.9)	(0.5)
Total fair value included in Financial instruments owned, at fair value
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	270.2	192.6
Total fair value included in Payables to clients
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	79.8	(1,392.4)
Total fair value included in Payables to broker-dealers, clearing organizations and counterparties
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	10.2	55.8
Fair value included in Financial instruments sold, not yet purchased, at fair value
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	288.3	384.0
Exchange-traded commodity derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1,907.0	4,520.4
Derivative liability, fair value, gross liability	1,890.3	4,519.3
OTC commodity derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1,523.3	756.9
Derivative liability, fair value, gross liability	1,456.0	695.6
Exchange-traded foreign exchange derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	4.3	25.6
Derivative liability, fair value, gross liability	4.3	25.7
OTC foreign exchange derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	497.1	577.1
Derivative liability, fair value, gross liability	455.3	549.3
Exchange-traded interest rate derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1,507.6	2,626.8
Derivative liability, fair value, gross liability	1,509.8	2,626.7
OTC interest rate derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	417.6	168.9
Derivative liability, fair value, gross liability	417.6	205.1
OTC interest rate derivatives | Designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative liability, fair value, gross liability	24.6	48.8
Exchange-traded equity index derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	2,140.9	609.5
Derivative liability, fair value, gross liability	2,140.9	609.5
OTC equity and indices derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	127.3	164.4
Derivative liability, fair value, gross liability	68.5	95.7
TBA and forward settling securities | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	73.5	207.6
Derivative liability, fair value, gross liability	47.5	154.9
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	24.6	48.8
Foreign currency forwards | Designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	1.7	0.0
Derivative liability, fair value, gross liability	$ 2.5	$ 21.8