Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - Narrative (Details) - USD ($) $ in Millions	3 Months Ended	6 Months Ended
	Dec. 31, 2022	Mar. 31, 2023	Sep. 30, 2022
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items]
Financial instruments sold, not yet purchased		$ 2,570.9	$ 2,469.6
Interest rate contracts
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items]
Maximum length of time hedged in cash flow hedge		2 years
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	2 years
Fair Value, Recurring | Derivatives
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items]
Financial instruments sold, not yet purchased		$ 209.7	$ 313.4