Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - Fair Values of Derivative Instruments Designated for Hedging Held (Details) - USD ($) $ in Millions	Dec. 31, 2021	Sep. 30, 2021
Derivatives, Fair Value [Line Items]
Asset Derivatives	$ 4,895.0	$ 5,760.7
Liability Derivatives	4,702.2	5,628.1
Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Asset Derivatives	0.1	0.0
Liability Derivatives	0.1	$ 0.0
Designated as Hedging Instrument \| Interest rate contracts \| Financial instruments owned, net
Derivatives, Fair Value [Line Items]
Asset Derivatives	0.1
Designated as Hedging Instrument \| Interest rate contracts \| Financial instruments sold, not yet purchased
Derivatives, Fair Value [Line Items]
Liability Derivatives	$ 0.1

Fair value, before effects of master netting arrangements, of a financial liability or 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. Includes liabilities elected not to be offset. Excludes liabilities not subject to a master netting arrangement.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 860
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-Section 50
-Paragraph 4D
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Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4B
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-URI http://asc.fasb.org/extlink&oid=125515794&loc=SL5624163-113959

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
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Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
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Reference 5: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
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-Section 55
-Paragraph 22
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226052-175313

Name:	us-gaap_DerivativeFairValueOfDerivativeLiability
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant