Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - TBAs and Forward Settling Securities (Details) - USD ($) $ in Millions	Mar. 31, 2022	Sep. 30, 2021
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	$ 12,036.2	$ 5,760.7
Derivative liability, fair value, gross liability	11,843.3	5,628.1
TBA Securities Purchased, Unrealized Gain | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	12.7	1.6
Derivative asset, notional amount	2,708.7	1,453.4
TBA Securities Purchased, Unrealized Loss | Payables to Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, notional amount	6,064.3	7,024.2
Derivative liability, fair value, gross liability	(78.8)	(37.6)
TBA Securities Sold, Unrealized Gain | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	118.6	43.0
Derivative liability, notional amount	(7,966.4)	(8,391.4)
TBA Securities Sold, Unrealized Loss | Payables to Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative liability, fair value, gross liability	(14.1)	(2.7)
Derivative liability, notional amount	(3,165.2)	(2,430.7)
Forward Settling Securities Purchased, Unrealized Gain | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	1.6	0.3
Derivative asset, notional amount	345.1	214.5
Forward Settling Securities Purchased, Unrealized Loss | Payables to Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, notional amount	2,413.4	2,580.7
Derivative liability, fair value, gross liability	(26.4)	(11.5)
Forward Setting Securities Sold, Unrealized Gain | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	19.3	14.1
Derivative liability, notional amount	(1,541.9)	(1,867.4)
Forward Setting Securities Sold, Unrealized Loss | Payables to Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative liability, fair value, gross liability	(0.9)	(0.4)
Derivative liability, notional amount	$ (373.3)	$ (133.1)