Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - TBAs and Forward Settling Securities (Details) - USD ($) $ in Millions	Dec. 31, 2021	Sep. 30, 2021
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	$ 4,895.0	$ 5,760.7
Derivative liability, fair value, gross liability	4,702.2	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	5.9	1.6
Derivative asset, notional amount	3,097.4	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	1,301.2	7,024.2
Derivative liability, fair value, gross liability	(1.9)	(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	6.9	43.0
Derivative liability, notional amount	(2,777.6)	(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	(7.2)	(2.7)
Derivative liability, notional amount	(3,740.9)	(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	0.8	0.3
Derivative asset, notional amount	1,216.2	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	505.8	2,580.7
Derivative liability, fair value, gross liability	(1.8)	(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	0.6	14.1
Derivative liability, notional amount	(615.4)	(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	(0.3)	(0.4)
Derivative liability, notional amount	$ (249.0)	$ (133.1)