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Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - Narrative (Details) - USD ($) $ in Millions | 6 Months Ended |
--- | --- | ---
Mar. 31, 2025 | Sep. 30, 2024
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items] |  |
Financial instruments sold, not yet purchased | $ 3,806.1 | $ 2,853.3
Foreign Currency Forward Contracts |  |
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items] |  |
Maximum length of time hedged in cash flow hedge | 2 years |
Fair Value, Recurring | Derivatives |  |
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items] |  |
Financial instruments sold, not yet purchased | $ 205.3 | 264.8
Fair Value, Recurring | Derivatives | Not Designated as Hedging Instrument |  |
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items] |  |
Financial instruments sold, not yet purchased | $ 205.3 | $ 264.8

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- Definition Fair value of obligations incurred from short sales. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2E -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2E Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 940 -SubTopic 320 -Name Accounting Standards Codification -Section 45 -Paragraph 2 -Publisher FASB -URI https://asc.fasb.org/1943274/2147479035/940-320-45-2 + Details
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- Definition Maximum length of time over which the entity is hedging its exposure to the variability in future cash flows for forecasted transactions, excluding those forecasted transactions related to the payment of variable interest on existing financial instruments, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (d) -SubTopic 30 -Topic 815 -Publisher FASB -URI https://asc.fasb.org/1943274/2147480870/815-30-50-1 + Details
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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 940 -SubTopic 320 -Name Accounting Standards Codification -Publisher FASB -URI https://asc.fasb.org/940-320/tableOfContent + Details
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