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Derivative Financial Instruments - Schedule of Derivative Instruments and Hedging Activities Disclosures (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Derivative Instruments Gain Loss [Line Items]      
Derivative, Excluded Component, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration] Nonoperating Income (Expense) Nonoperating Income (Expense) Nonoperating Income (Expense)
Foreign Exchange Forward Contract and Options | Not Designated as Hedging Instrument | Other income, net      
Derivative Instruments Gain Loss [Line Items]      
Net realized and unrealized gain (loss), excluding the underlying foreign currency exposure being hedged $ 11,950 $ (3,758) $ 3,518
Foreign Exchange Forward | Designated as Hedging Instrument | Net Investment Hedging      
Derivative Instruments Gain Loss [Line Items]      
Net realized and unrealized gain (loss), excluding the underlying foreign currency exposure being hedged (1,478) 695 (5,483)
Gain (loss) reclassified from OCI—effective portion (17,466) 2,723 109
Gain recognized—portion excluded from effectiveness testing $ 1,862 $ 1,249 $ 3,506