Condensed Consolidated Statements of Cash Flows - USD ($) $ in Millions		9 Months Ended
		Jun. 30, 2023	Jun. 30, 2022
Cash flows from operating activities:
Net income		$ 187.8	$ 154.8
Adjustments to reconcile net income to net cash used in operating activities:
Depreciation and amortization		39.6	32.1
Amortization of right of use assets		7.9	12.1
Bad debts, net of recoveries		10.0	11.4
Deferred income taxes		3.2	0.4
Amortization of debt issuance costs		4.3	3.5
Amortization of share-based compensation		21.3	12.8
Gain on acquisition		(23.5)	0.0
Changes in operating assets and liabilities, net:
Securities and other assets segregated under federal and other regulations		600.6	(7.3)
Securities purchased under agreements to resell		(970.0)	523.7
Securities borrowed		115.5	1,054.4
Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net		(1,072.7)	(2,931.3)
Receivables from clients, net		(89.8)	(176.7)
Notes receivable, net		(0.2)	1.1
Income taxes receivable		(5.3)	17.4
Financial instruments owned, at fair value		(1,112.6)	621.1
Physical commodities inventory, net		91.3	(117.9)
Other assets		(44.5)	(12.4)
Accounts payable and other accrued liabilities		23.5	36.4
Operating lease liabilities		(0.5)	(13.3)
Payables to clients		(170.7)	2,311.0
Payables to broker-dealers, clearing organizations, and counterparties		(26.6)	(182.8)
Income taxes payable		18.8	11.8
Securities sold under agreements to repurchase		1,833.9	(1,533.2)
Securities loaned		(96.2)	(1,058.1)
Financial instruments sold, not yet purchased, at fair value		260.1	733.0
Net cash used in operating activities		(394.8)	(496.0)
Cash flows from investing activities:
Acquisition of businesses and assets, net of cash received		(6.1)	(0.2)
Sale of exchange memberships and common stock		0.0	0.2
Purchases of property and equipment		(32.8)	(37.6)
Net cash used in investing activities		(38.9)	(37.6)
Cash flows from financing activities:
Net change in payables to lenders under loans with maturities 90 days or less		(37.7)	269.6
Proceeds from payables to lenders under loans with maturities greater than 90 days		170.0	452.0
Repayments of payables to lenders under loans with maturities greater than 90 days		(205.0)	(462.0)
Repayments of senior secured term loan		0.0	(170.3)
Deferred payments on acquisitions		(18.5)	(1.5)
Payment of contingent consideration		0.0	(2.8)
Exercise of stock options		3.6	6.2
Net cash (used in)/provided by financing activities		(87.6)	91.2
Effect of exchange rates on cash, segregated cash, cash equivalents, and segregated cash equivalents		14.8	(5.5)
Net decrease in cash, segregated cash, cash equivalents, and segregated cash equivalents		(506.5)	(447.9)
Cash, segregated cash, cash equivalents, and segregated cash equivalents at beginning of period		6,285.1	6,509.5
Cash, segregated cash, cash equivalents, and segregated cash equivalents at end of period		5,778.6	6,061.6
Supplemental disclosure of cash flow information:
Cash paid for interest		550.8	85.4
Income taxes paid, net of cash refunds		41.9	25.4
Supplemental disclosure of non-cash investing and financing activities:
Identified intangible assets and goodwill on acquisitions		10.6	0.0
Additional consideration payable related to acquisitions, net		28.7	0.0
Acquisition of business:
Assets acquired		141.6	0.0
Liabilities assumed		84.1	0.0
Total net assets acquired		57.5	0.0
Cash and cash equivalents		1,401.3	1,363.7
Cash segregated under federal and other regulations	[1]	2,487.5	2,522.3
Securities segregated under federal and other regulations	[1]	0.1	0.1
Cash segregated and deposited with or pledged to exchange-clearing organizations and other futures commission merchants (“FCMs”)	[2]	1,499.2	1,910.0
Securities segregated and pledged to exchange-clearing organizations	[2]	390.5	265.5
Total cash, segregated cash, cash equivalents, and segregated cash equivalents shown in the condensed consolidated statements of cash flows		5,778.6	6,061.6
Non-cash equivalent segregated assets		4.8	21.4
Non-segregated cash and other non-cash equivalent assets included within deposits and receivables from broker-dealers, clearing organizations, and counterparties		$ 5,408.0	$ 5,084.6

[1] Represents segregated client cash held at third-party banks. Excludes segregated commodity warehouse receipts, segregated U.S. Treasury obligations with original or acquired maturities of greater than 90 days, and other assets of $4.8 million and $21.4 million as of June 30, 2023 and 2022, respectively, included within Cash, securities and other assets segregated under federal and other regulations on the Condensed Consolidated Balance Sheets.

[2] Represents segregated client cash and U.S. Treasury obligations on deposit with, or pledged to, exchange clearing organizations and other FCMs. Excludes non-segregated cash, segregated U.S. Treasury obligations pledged to exchange-clearing organizations with original or acquired maturities greater than 90 days, and other assets of $5,408.0 million and $5,084.6 million as of June 30, 2023 and 2022, respectively, included within Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net on the Condensed Consolidated Balance Sheets.