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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 | Sep. 30, 2021 | Sep. 30, 2020
--- | --- | ---
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | $ 5,760.7 | $ 3,264.4
Derivative liability, fair value, gross liability | 5,628.1 | 3,069.5
TBA Securities Purchased, Unrealized Gain | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 1.6 | 10.8
Derivative asset, notional amount | 1,453.4 | 5,389.3
TBA Securities Purchased, Unrealized Loss | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties |  |
Derivatives, Fair Value [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 |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 37.6 | 0.0
Derivative asset, notional amount | 7,024.2 | 0.0
TBA Securities Sold, Unrealized Gain | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties |  |
Derivatives, Fair Value [Line Items] |  |
Derivative liability, fair value, gross liability | 43.0 | 0.0
Derivative liability, notional amount | (8,391.4) | 0.0
TBA Securities Sold, Unrealized Gain | Payables to Broker-dealers, Clearing Organizations and Counterparties |  |
Derivatives, Fair Value [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 | Payables to Broker-dealers, Clearing Organizations and Counterparties |  |
Derivatives, Fair Value [Line Items] |  |
Derivative liability, fair value, gross liability | 2.7 | 13.0
Derivative liability, notional amount | (2,430.7) | (6,549.4)
Forward Settling Securities Purchased, Unrealized Gain | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | (0.3) | 0.0
Derivative asset, notional amount | 214.5 | 0.0
Forward Settling Securities Purchased, Unrealized Loss | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | 0.0 | 7.3
Derivative asset, notional amount | 0.0 | 2,447.1
Forward Settling Securities Purchased, Unrealized Loss | Payables to Broker-dealers, Clearing Organizations and Counterparties |  |
Derivatives, Fair Value [Line Items] |  |
Derivative asset, fair value, gross asset | (11.5) | 0.0
Derivative asset, notional amount | 2,580.7 | 0.0
Forward Settling Securities Sold, Unrealized Gain | Deposits and Receivables from Broker-dealers, Clearing Organizations and Counterparties |  |
Derivatives, Fair Value [Line Items] |  |
Derivative liability, fair value, gross liability | (14.1) | (17.4)
Derivative liability, notional amount | (1,867.4) | (1,946.0)
Forward Settling Securities Sold, Unrealized Loss | Payables to Broker-dealers, Clearing Organizations and Counterparties |  |
Derivatives, Fair Value [Line Items] |  |
Derivative liability, fair value, gross liability | (0.4) | 0.0
Derivative liability, notional amount | $ (133.1) | $ 0.0

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