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 |