Condensed Consolidated Statements of Cash Flows (Unaudited) - USD ($) $ in Millions		6 Months Ended
		Mar. 31, 2024	Mar. 31, 2023
Cash flows from operating activities:
Net income		$ 122.2	$ 118.3
Adjustments to reconcile net income to net cash provided by/(used in) operating activities:
Depreciation and amortization		23.5	25.8
Amortization of right of use assets		9.1	5.7
Bad debts (recoveries), net		(0.7)	3.7
Deferred income taxes		(3.3)	1.8
Amortization of debt issuance costs		2.6	2.8
Amortization of share-based compensation		16.8	14.9
Gain on acquisition		0.0	(23.5)
Changes in operating assets and liabilities, net:
Securities and other assets segregated under federal and other regulations		1.7	579.6
Securities purchased under agreements to resell		(765.1)	(951.2)
Securities borrowed		(301.5)	456.1
Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net		133.2	(1,314.1)
Receivables from clients, net		(609.6)	(363.3)
Income taxes receivable		(7.7)	3.7
Financial instruments owned, at fair value		(616.3)	(859.3)
Physical commodities inventory, net		(79.6)	(36.1)
Other assets		(68.7)	(45.2)
Accounts payable and other accrued liabilities		(41.7)	60.1
Operating lease liabilities		(0.8)	(0.5)
Payables to clients		1,189.4	274.1
Payables to broker-dealers, clearing organizations, and counterparties		(50.7)	(101.8)
Income taxes payable		(1.5)	9.2
Securities sold under agreements to repurchase		1,485.1	1,827.5
Securities loaned		341.3	(425.0)
Financial instruments sold, not yet purchased, at fair value		158.7	134.0
Net cash provided by/(used in) operating activities		936.4	(602.7)
Cash flows from investing activities:
Proceeds from notes receivable		5.0	0.0
Acquisition of businesses and assets, net of cash received		(1.1)	(6.1)
Sale of exchange memberships and common stock		0.1	0.0
Purchases of property and equipment		(30.1)	(22.5)
Net cash used in investing activities		(26.1)	(28.6)
Cash flows from financing activities:
Net change in payables to lenders under loans with maturities 90 days or less		(87.4)	67.0
Proceeds from payables to lenders under loans with maturities greater than 90 days		0.0	150.0
Repayments of payables to lenders under loans with maturities greater than 90 days		0.0	(151.0)
Proceeds from issuance of senior secured notes		550.0	0.0
Deferred payments on acquisitions		0.0	(17.2)
Debt issuance costs		(7.9)	0.0
Shares withheld to cover taxes on vesting of equity awards		(1.2)	0.0
Exercise of stock options		3.5	3.6
Net cash provided by financing activities		457.0	52.4
Effect of exchange rates on cash, restricted cash, segregated cash, cash equivalents, and segregated cash equivalents		2.2	11.1
Net increase/(decrease) in cash, restricted cash, segregated cash, cash equivalents, and segregated cash equivalents		1,369.5	(567.8)
Cash, restricted cash, segregated cash, cash equivalents, and segregated cash equivalents at beginning of period		6,041.7	6,285.1
Cash, restricted cash, segregated cash, cash equivalents, and segregated cash equivalents at end of period		7,411.2	5,717.3
Supplemental disclosure of cash flow information:
Cash paid for interest		548.6	337.5
Income taxes paid, net of cash refunds		56.0	19.5
Supplemental disclosure of non-cash investing and financing activities:
Additional consideration payable related to acquisition of customer list		0.8	0.0
Identified intangible assets and goodwill on acquisitions		0.0	10.3
Additional consideration payable related to acquisitions, net		0.0	28.7
Acquisition of business:
Assets acquired		0.0	143.0
Liabilities assumed		0.0	84.1
Total net assets acquired		0.0	58.9
Cash and cash equivalents		1,305.1	1,263.9
Restricted cash	[1]	363.0	0.0
Cash segregated under federal and other regulations	[2]	2,834.3	2,486.4
Securities segregated under federal and other regulations	[2]	0.0	0.2
Cash segregated and deposited with or pledged to exchange-clearing organizations and other futures commission merchants (“FCMs”)	[3]	1,362.9	1,032.5
Securities segregated and pledged to exchange-clearing organizations	[3]	1,545.9	934.3
Total cash, restricted cash, segregated cash, cash equivalents, and segregated cash equivalents shown in the condensed consolidated statements of cash flows		7,411.2	5,717.3
Non-cash equivalent segregated assets		4.1	25.7
Non-segregated cash and other non-cash equivalent assets included within deposits and receivables from broker-dealers, clearing organizations, and counterparties		$ 4,797.7	$ 5,649.5

[1] Represents restricted cash held in an escrow account, as further described in Note 1 and Note 9.

[2] 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 $4.1 million and $25.7 million as of March 31, 2024 and 2023, respectively, included within Cash, securities and other assets segregated under federal and other regulations on the Condensed Consolidated Balance Sheets.

[3] 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 $4,797.7 million and $5,649.5 million as of March 31, 2024 and 2023, respectively, included within Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net on the Condensed Consolidated Balance Sheets.