Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - Narrative (Details) - USD ($) $ in Millions	6 Months Ended
	Mar. 31, 2024	Sep. 30, 2023
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items]
Financial instruments sold, not yet purchased	$ 3,223.0	$ 3,085.6
Interest rate contracts
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items]
Maximum length of time hedged in cash flow hedge	1 year
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	$ 436.7	261.2
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	$ 436.7	$ 261.2