Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022
Derivatives, Fair Value [Line Items]
Financial instruments sold, not yet purchased, at fair value	$ 3,085.6	$ 2,469.6
Interest rate contracts
Derivatives, Fair Value [Line Items]
Maximum length of time hedged in cash flow hedge (in years)	1 year
Foreign currency forwards
Derivatives, Fair Value [Line Items]
Maximum length of time hedged in cash flow hedge (in years)	2 years
Fair Value, Measurements, Recurring | Derivatives
Derivatives, Fair Value [Line Items]
Financial instruments sold, not yet purchased, at fair value	$ 261.2	$ 313.4
Fair Value, Measurements, Recurring | Not designated as hedging instrument | Derivatives
Derivatives, Fair Value [Line Items]
Financial instruments sold, not yet purchased, at fair value	$ 261.2