Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - TBAs and Forward Settling Securities (Details) - USD ($) $ in Millions	Mar. 31, 2021	Sep. 30, 2020
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	$ 4,622.0	$ 3,264.4
Derivative liability, fair value, gross liability	4,606.5	3,069.5
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	0.0	10.8
Derivative asset, notional amount	0.0	5,389.3
TBA Securities Purchased, Unrealized Gain | Payables to Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	1.3	0.0
Derivative asset, notional amount	1,336.0	0.0
TBA Securities Purchased, Unrealized Loss | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	0.0	(1.7)
Derivative asset, notional amount	0.0	2,647.7
TBA Securities Purchased, Unrealized Loss | Payables to Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	(45.0)	0.0
Derivative asset, notional amount	7,005.0	0.0
TBA Securities Sold, Unrealized Gain | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative liability, fair value, gross liability	52.2	0.0
Derivative liability, notional amount	(8,409.0)	0.0
TBA Securities Sold, Unrealized Gain | Payables to Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative liability, fair value, gross liability	0.0	2.8
Derivative liability, notional amount	0.0	(2,978.7)
TBA Securities Sold, Unrealized Loss | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative liability, fair value, gross liability	(1.5)	0.0
Derivative liability, notional amount	(1,688.0)	0.0
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	0.0	(13.0)
Derivative liability, notional amount	0.0	(6,549.4)
Forward Settling Securities Sold, Unrealized Gain | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative liability, fair value, gross liability	1.4	17.4
Derivative liability, notional amount	(2,032.0)	(1,946.0)
Forward Settling Securities Purchased, Unrealized Loss | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	(1.0)	(7.3)
Derivative asset, notional amount	$ 2,866.0	$ 2,447.1