Financial Instruments with Off-Balance Sheet Risk and Concentrations of Credit Risk - TBAs and Forward Settling Securities (Details) - USD ($) $ in Millions	Jun. 30, 2021	Sep. 30, 2020
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	$ 5,640.0	$ 3,264.4
Derivative liability, fair value, gross liability	5,302.5	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	9.2	0.0
Derivative asset, notional amount	3,030.2	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	(2.8)	0.0
Derivative asset, notional amount	1,616.2	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	4.6	0.0
Derivative liability, notional amount	(2,777.2)	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	(9.3)	0.0
Derivative liability, notional amount	(3,433.8)	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 Purchased | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties
Derivative Instruments and Hedging Activities Disclosure [Line Items]
Derivative asset, fair value, gross asset	7.8	0.0
Derivative asset, notional amount	1,579.0	0.0
Forward Setting 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	(4.4)	0.0
Derivative liability, notional amount	(892.8)	0.0
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	0.0	17.4
Derivative liability, notional amount	0.0	(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	0.0	(7.3)
Derivative asset, notional amount	$ 0.0	$ 2,447.1