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Acquisitions - Cotton Distributors Inc. (Details) - USD ($) $ in Millions |  | 3 Months Ended | 6 Months Ended
--- | --- | --- | ---
Oct. 31, 2022 | Mar. 31, 2023 | Mar. 31, 2022 | Mar. 31, 2023 | Mar. 31, 2022
Business Acquisition [Line Items] |  |  |  |  |
Net operating revenues |  | $ 399.4 | $ 400.3 | $ 781.4 | $ 714.1
Net income |  | 41.7 | $ 64.0 | 118.3 | 105.7
Identifiable intangible assets acquired |  |  |  |  |
Gain on acquisition |  |  |  | 23.5 | $ 0.0
Cotton Distributors Inc. |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |
Consideration transferred | $ 42.7 |  |  |  |
Net operating revenues |  | (1.7) |  | 12.3 |
Net income |  | $ (4.1) |  | $ 5.1 |
Identifiable intangible assets acquired |  |  |  |  |
Cash and cash equivalents | 8.2 |  |  |  |
Deposits with and receivables from broker-dealers, clearing organizations, and counterparties | 7.7 |  |  |  |
Receivables from clients, net | 51.9 |  |  |  |
Financial instruments owned, at fair value | 45.7 |  |  |  |
Deferred income taxes, net | (3.3) |  |  |  |
Property and equipment, net | 0.1 |  |  |  |
Physical commodities inventory, net | 22.5 |  |  |  |
Other assets | 6.7 |  |  |  |
Total fair value of tangible assets acquired | 139.5 |  |  |  |
Accounts payable and other accrued liabilities | 40.0 |  |  |  |
Financial instruments sold, not yet purchased, at fair value | 28.3 |  |  |  |
Payables to lenders under loans | 10.1 |  |  |  |
Payable to broker-dealers, clearing organizations, and counterparties | 0.4 |  |  |  |
Payable to clients | 2.6 |  |  |  |
Income taxes payable | 0.8 |  |  |  |
Total fair value of tangible liabilities assumed | 82.2 |  |  |  |
Fair value of tangible net assets acquired | 57.3 |  |  |  |
Total fair value of intangible assets acquired | 8.9 |  |  |  |
Fair value of identifiable net assets acquired | 66.2 |  |  |  |
Total merger consideration | 42.7 |  |  |  |
Gain on acquisition | 23.5 |  |  |  |
Cotton Distributors Inc. | Client relationships |  |  |  |  |
Identifiable intangible assets acquired |  |  |  |  |
Total fair value of intangible assets acquired | 4.7 |  |  |  |
Cotton Distributors Inc. | Supplier relationships |  |  |  |  |
Identifiable intangible assets acquired |  |  |  |  |
Total fair value of intangible assets acquired | 3.7 |  |  |  |
Cotton Distributors Inc. | Trade name |  |  |  |  |
Identifiable intangible assets acquired |  |  |  |  |
Total fair value of intangible assets acquired | 0.4 |  |  |  |
Cotton Distributors Inc. | Non-compete |  |  |  |  |
Identifiable intangible assets acquired |  |  |  |  |
Total fair value of intangible assets acquired | $ 0.1 |  |  |  |

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