Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - Narrative (Details) - USD ($)	6 Months Ended
	Mar. 31, 2022	Sep. 30, 2021
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items]
Financial instruments sold, not yet purchased	$ 2,781,800,000	$ 1,771,200,000
Derivative instruments, gain (loss) recognized in income, net	$ 1,600,000
Interest Rate Swap
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items]
Maximum length of time hedged in cash flow hedge	2 years
Derivative, notional amount	$ 1,000,000,000
Fair Value, Recurring | Derivatives
Security Owned and Sold, Not yet Purchased, at Fair Value [Line Items]
Financial instruments sold, not yet purchased	$ 484,400,000	$ 368,500,000