Condensed Consolidated Statements of Cash Flows - USD ($) $ in Millions		6 Months Ended
		Mar. 31, 2023	Mar. 31, 2022
Cash flows from operating activities:
Net income		$ 118.3	$ 105.7
Adjustments to reconcile net income to net cash provided (used in)/provided by operating activities:
Depreciation and amortization		25.8	20.4
Amortization of right of use assets		5.7	7.8
Bad debts, net of recoveries		3.7	12.1
Deferred income taxes		1.8	(0.4)
Amortization of debt issuance costs		2.8	2.2
Amortization of share-based compensation		14.9	8.3
Gain on acquisition		(23.5)	0.0
Changes in operating assets and liabilities, net:
Securities and other assets segregated under federal and other regulations		579.6	(11.5)
Securities purchased under agreements to resell		(951.2)	(290.7)
Securities borrowed		456.1	78.3
Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net		(1,314.1)	202.3
Receivables from clients, net		(363.3)	(126.7)
Notes receivable, net		0.0	1.0
Income taxes receivable		3.7	10.6
Financial instruments owned, at fair value		(859.3)	198.4
Physical commodities inventory, net		(36.1)	(134.5)
Other assets		(45.2)	6.8
Accounts payable and other accrued liabilities		60.1	31.6
Operating lease liabilities		(0.5)	(6.8)
Payables to clients		274.1	1,661.9
Payables to broker-dealers, clearing organizations, and counterparties		(101.8)	(93.6)
Income taxes payable		9.2	15.4
Securities sold under agreements to repurchase		1,827.5	(533.0)
Securities loaned		(425.0)	(49.9)
Financial instruments sold, not yet purchased, at fair value		134.0	986.3
Net cash (used in)/provided by operating activities		(602.7)	2,102.0
Cash flows from investing activities:
Acquisition of businesses and assets, net of cash received		(6.1)	0.0
Sale of exchange memberships and common stock		0.0	0.2
Purchases of property and equipment		(22.5)	(24.3)
Net cash used in investing activities		(28.6)	(24.1)
Cash flows from financing activities:
Net change in payables to lenders under loans with maturities 90 days or less		67.0	232.7
Proceeds from payables to lenders under loans with maturities greater than 90 days		150.0	430.0
Repayments of payables to lenders under loans with maturities greater than 90 days		(151.0)	(440.0)
Repayments of senior secured term loan		0.0	(4.9)
Deferred payments on acquisitions		(17.2)	(1.5)
Exercise of stock options		3.6	5.9
Net cash provided by financing activities		52.4	222.2
Effect of exchange rates on cash, segregated cash, cash equivalents, and segregated cash equivalents		11.1	(0.1)
Net (decrease)/increase in cash, segregated cash, cash equivalents, and segregated cash equivalents		(567.8)	2,300.0
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		5,717.3	8,809.5
Supplemental disclosure of cash flow information:
Cash paid for interest		337.5	43.9
Income taxes paid, net of cash refunds		19.5	7.8
Supplemental disclosure of non-cash investing and financing activities:
Identified intangible assets and goodwill on acquisitions		10.3	0.0
Additional consideration payable related to acquisitions, net		28.7	0.0
Acquisition of business:
Assets acquired		143.0	0.0
Liabilities assumed		84.1	0.0
Total net assets acquired		58.9	0.0
Cash and cash equivalents		1,263.9	1,299.7
Cash segregated under federal and other regulations	[1]	2,486.4	2,740.9
Securities segregated under federal and other regulations	[1]	0.2	0.0
Cash segregated and deposited with or pledged to exchange-clearing organizations and other futures commission merchants (“FCMs”)	[2]	1,032.5	4,294.1
Securities segregated and pledged to exchange-clearing organizations	[2]	934.3	474.8
Total cash, segregated cash, cash equivalents, and segregated cash equivalents shown in the condensed consolidated statements of cash flows		5,717.3	8,809.5
Non-cash equivalent segregated assets		25.7	25.6
Non-segregated cash and other non-cash equivalent assets included within deposits and receivables from broker-dealers, clearing organizations, and counterparties		$ 5,649.5	$ 1,951.0

[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 $25.7 million and $25.6 million as of March 31, 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 $5,649.5 million and $1,951.0 million as of March 31, 2023 and 2022, respectively, included within Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net on the Condensed Consolidated Balance Sheets.