Consolidated Statements of Cash Flows - USD ($) $ in Millions		12 Months Ended
		Sep. 30, 2024	Sep. 30, 2023		Sep. 30, 2022
Cash flows from operating activities:
Net income		$ 260.8	$ 238.5		$ 207.1
Adjustments to reconcile net income to net cash provided by/(used in) operating activities:
Depreciation and amortization		53.1	51.0		44.4
Amortization of operating right of use assets		21.5	14.0		15.9
Provision for bad debts, net of recoveries		0.6	16.5		15.8
Deferred income taxes		(10.5)	(2.4)		(0.3)
Loss on extinguishment of debt		3.7	0.0		0.0
Amortization and extinguishment of debt issuance costs		5.4	5.8		4.5
Actuarial adjustment on pension and postretirement benefits		0.1	0.3		(0.1)
Amortization of share-based compensation expense		37.2	28.0		17.8
Gain on acquisition		0.0	(23.5)		0.0
Changes in operating assets and liabilities, net:
Securities and other assets segregated under federal and other regulations		(46.0)	599.5		(591.5)
Securities purchased under agreements to resell		(2,222.0)	(1,307.5)		567.9
Securities borrowed		(533.2)	80.7		953.3
Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net		262.5	(595.6)		(2,174.3)
Receivable from clients, net		(330.3)	(80.5)		(119.7)
Notes receivable, net		0.2	(0.1)		1.0
Income taxes receivable		7.2	(13.4)		10.4
Financial instruments owned, at fair value		(1,714.4)	(857.9)		187.3
Physical commodities inventory, net		(144.1)	(1.3)		(67.2)
Other assets		(119.8)	(60.4)		(9.8)
Accounts payable and other accrued liabilities		(5.3)	82.5		101.4
Operating lease liabilities		(9.8)	(8.0)		(16.0)
Payable to clients		369.9	81.4		2,055.1
Payable to broker-dealers, clearing organizations and counterparties		291.8	(217.8)		46.3
Income taxes payable		(19.6)	29.3		2.8
Securities sold under agreements to repurchase		4,054.7	1,331.0		(1,145.3)
Securities loaned		498.6	(72.2)		(964.1)
Financial instruments sold, not yet purchased, at fair value		(205.4)	658.4		627.8
Net cash provided by/(used in) operating activities		506.9	(23.7)		(229.5)
Cash flows from investing activities:
Collection of notes receivable		5.0	0.0		0.0
Proceeds from stock sales of clearing organization memberships		0.0	0.0		0.2
Cash paid for acquisitions of businesses and assets, net of cash acquired		(2.3)	(6.1)		(0.2)
Purchase of exchange memberships and common stock		(1.2)	0.0		0.0
Purchase of property and equipment and internally developed software		(65.2)	(46.9)		(49.5)
Net cash used in investing activities		(63.7)	(53.0)		(49.5)
Cash flows from financing activities:
Net change in lenders under loans with maturities 90 days or less		(2.2)	(119.3)		211.5
Proceeds from lenders under loans with maturities greater than 90 days		10.0	187.0		547.0
Repayments of lenders under loans with maturities greater than 90 days		(10.0)	(222.0)		(522.0)
Repayments of senior secured term loan		0.0	0.0		(170.3)
Proceeds from issuance of senior secured notes		550.0	0.0		0.0
Repayment of senior secured notes		(347.9)	0.0		(0.5)
Deferred payments on acquisitions		(9.6)	(18.7)		(3.0)
Payment of contingent consideration		0.0	0.0		(3.6)
Debt issuance costs		(7.7)	0.0		0.0
Shares withheld to cover taxes on vesting of equity awards		(2.3)	0.0		0.0
Exercise of stock options		7.7	3.7		6.7
Net cash provided by/(used in) financing activities		188.0	(169.3)		65.8
Effect of exchange rates on cash, segregated cash, cash equivalents, and segregated cash equivalents		(0.3)	2.6		(11.2)
Net increase/(decrease) in cash, segregated cash, cash equivalents, and segregated cash equivalents		630.9	(243.4)		(224.4)
Cash, segregated cash, cash equivalents, and segregated cash equivalents at beginning of period		6,041.7	6,285.1		6,509.5
Cash, segregated cash, cash equivalents, and segregated cash equivalents at end of period		6,672.6	6,041.7		6,285.1
Supplemental disclosure of cash flow information:
Cash paid for interest		1,230.2	786.5		149.2
Income taxes paid, net of cash refunds		117.8	71.0		56.3
Supplemental disclosure of non-cash investing and financing activities:
Identified intangible assets and goodwill on acquisitions		5.6	10.6		0.2
Additional consideration payable related to acquisitions		3.7	11.1		0.0
Acquisition of businesses:
Assets acquired		0.7	141.6		0.0
Liabilities acquired		0.6	84.1		0.0
Total net assets acquired		0.1	57.5		0.0
Cash and cash equivalents		1,269.0	1,108.3		1,108.5
Cash segregated under federal and other regulations	[1]	2,789.4	2,420.5		2,461.6
Securities segregated under federal and other regulations	[1]	0.0	0.0		200.0
Cash segregated and deposited with or pledged to exchange-clearing organizations and other futures commission merchants (“FCMs”)	[2]	1,688.5	1,256.5		2,138.2
Securities segregated and pledged to exchange-clearing organizations	[2]	925.7	1,256.4		376.8
Total cash, segregated cash, cash equivalents and segregated cash equivalents shown in the consolidated statements of cash flows		6,672.6	6,041.7		6,285.1
Non cash equivalent segregated assets		51.8	5.8	[1]	605.6
Non segregated cash and other non cash equivalent assets included with in deposits and receivables from broker dealers clearing organizations and counter parties		$ 4,669.0	$ 4,930.9		$ 4,327.6

[1] Represents segregated client cash held at third-party banks. Excludes segregated commodity warehouse receipts, segregated United States (“U.S.”) Treasury obligations with original or acquired maturities of greater than 90 days, and other assets, combined totaling $51.8 million, $5.8 million, and $605.6 million as of September 30, 2024, 2023, and 2022, respectively, included within Cash, securities and other assets segregated under federal and other regulations on the 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 securities pledged to exchange-clearing organizations with original or acquired maturities greater than 90 days, and other assets, combined totaling $4,669.0 million, $4,930.9 million, and $4,327.6 million as of September 30, 2024, 2023, and 2022, respectively, included within Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net on the Consolidated Balance Sheets.