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, 2022 USD ($) contract	Sep. 30, 2021 USD ($) contract
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	$ 9,657.2	$ 5,760.7
Derivative liability, fair value, gross liability	9,552.4	5,628.1
Impact of netting and collateral asset	(10,920.8)	(5,353.9)
Impact of netting and collateral liability	$ (10,505.0)	$ (4,955.4)
Derivative, number of instruments held | contract	13.3	11.1
Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	$ 9,657.2	$ 5,760.7
Derivative liability, fair value, gross liability	9,481.8	5,628.1
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	70.6	0.0
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	(1,455.7)	259.9
Total fair value included in Receivables from clients, net
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	(0.5)	2.6
Total fair value included in Financial instruments owned, at fair value
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	192.6	144.3
Total fair value included in Payables to clients
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	(1,392.4)	291.5
Total fair value included in Payables to broker-dealers, clearing organizations and counterparties
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	55.8	12.7
Fair value included in Financial instruments sold, not yet purchased, at fair value
Derivatives, Fair Value [Line Items]
Derivative, fair value, net	384.0	368.5
Exchange-traded commodity derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	4,520.4	3,904.1
Derivative liability, fair value, gross liability	4,519.3	3,904.7
OTC commodity derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	756.9	803.4
Derivative liability, fair value, gross liability	695.6	761.3
Exchange-traded foreign exchange derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	25.6	119.9
Derivative liability, fair value, gross liability	25.7	119.9
OTC foreign exchange derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	577.1	216.9
Derivative liability, fair value, gross liability	549.3	185.5
Exchange-traded interest rate derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	2,626.8	245.9
Derivative liability, fair value, gross liability	2,626.7	249.0
OTC interest rate derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	168.9	56.4
Derivative liability, fair value, gross liability	205.1	54.9
OTC interest rate derivatives | Designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative liability, fair value, gross liability	48.8
Exchange-traded equity index derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	609.5	206.5
Derivative liability, fair value, gross liability	609.5	206.5
OTC equity and indices derivatives | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	164.4	148.5
Derivative liability, fair value, gross liability	95.7	94.1
TBA and forward settling securities | Not designated as hedging instrument
Derivatives, Fair Value [Line Items]
Derivative asset, fair value, gross asset	207.6	59.1
Derivative liability, fair value, gross liability	154.9	52.2
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	48.8	0.0
Foreign currency forwards | 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	$ 21.8	$ 0.0