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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
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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

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