Consolidated Statements of Cash Flows - USD ($) $ in Millions		12 Months Ended
		Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Cash flows from operating activities:
Net income		$ 238.5	$ 207.1	$ 116.3
Adjustments to reconcile net income to net cash (used in)/provided by operating activities:
Depreciation and amortization		51.0	44.4	36.5
Amortization of operating right of use assets		14.0	15.9	12.2
Provision for bad debts, net of recoveries		16.5	15.8	10.4
Deferred income taxes		(2.4)	(0.3)	3.2
Amortization and extinguishment of debt issuance costs		5.8	4.5	3.9
Actuarial adjustment on pension and postretirement benefits		0.3	(0.1)	(0.3)
Amortization of share-based compensation expense		28.0	17.8	13.9
Gain on acquisition		(23.5)	0.0	(3.3)
Gain on stock sales of clearing organization memberships		0.0	0.0	(0.7)
Changes in operating assets and liabilities, net:
Securities and other assets segregated under federal and other regulations		599.5	(591.5)	(1.0)
Securities purchased under agreements to resell		(1,307.5)	567.9	(543.7)
Securities borrowed		80.7	953.3	(723.1)
Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net		(595.6)	(2,174.3)	(132.0)
Receivable from clients, net		(80.5)	(119.7)	(68.3)
Notes receivable, net		(0.1)	1.0	(4.4)
Income taxes receivable		(13.4)	10.4	(9.6)
Financial instruments owned, at fair value		(857.9)	187.3	(1,626.9)
Physical commodities inventory, net		(1.3)	(67.2)	(166.4)
Other assets		(60.4)	(9.8)	(16.7)
Accounts payable and other accrued liabilities		82.5	101.4	35.7
Operating lease liabilities		(8.0)	(16.0)	(8.6)
Payable to clients		81.4	2,055.1	2,146.7
Payable to broker-dealers, clearing organizations and counterparties		(217.8)	46.3	76.0
Income taxes payable		29.3	2.8	(9.4)
Securities sold under agreements to repurchase		1,331.0	(1,145.3)	1,185.4
Securities loaned		(72.2)	(964.1)	711.7
Financial instruments sold, not yet purchased, at fair value		658.4	627.8	1,085.2
Net cash (used in)/provided by operating activities		(23.7)	(229.5)	2,122.7
Cash flows from investing activities:
Proceeds from stock sales of clearing organization memberships		0.0	0.2	1.6
Cash paid for acquisitions, net of cash acquired		(6.1)	(0.2)	(2.4)
Sale of property and equipment		0.0	0.0	3.1
Purchase of property and equipment and internally developed software		(46.9)	(49.5)	(62.1)
Net cash used in investing activities		(53.0)	(49.5)	(59.8)
Cash flows from financing activities:
Net change in lenders under loans with maturities 90 days or less		(119.3)	211.5	(33.5)
Proceeds from lenders under loans with maturities greater than 90 days		187.0	547.0	191.4
Repayments of lenders under loans with maturities greater than 90 days		(222.0)	(522.0)	(186.4)
Repayments of senior secured term loan		0.0	(170.3)	(9.8)
Repayment of senior secured notes		0.0	(0.5)	(1.6)
Issuance of note payable		0.0	0.0	9.0
Deferred payments on acquisitions		(18.7)	(3.0)	(2.2)
Payment of contingent consideration		0.0	(3.6)	0.0
Share repurchase		0.0	0.0	(11.7)
Exercise of stock options		3.7	6.7	9.2
Net cash (used in)/provided by financing activities		(169.3)	65.8	(35.6)
Effect of exchange rates on cash, segregated cash, cash equivalents, and segregated cash equivalents		2.6	(11.2)	13.8
Net (decrease)/increase in cash, segregated cash, cash equivalents, and segregated cash equivalents		(243.4)	(224.4)	2,041.1
Cash, segregated cash, cash equivalents, and segregated cash equivalents at beginning of period		6,285.1	6,509.5	4,468.4
Cash, segregated cash, cash equivalents, and segregated cash equivalents at end of period		6,041.7	6,285.1	6,509.5
Supplemental disclosure of cash flow information:
Cash paid for interest		786.5	149.2	87.0
Income taxes paid, net of cash refunds		71.0	56.3	52.0
Supplemental disclosure of non-cash investing and financing activities:
Identified intangible assets and goodwill on acquisitions		10.6	0.2	6.5
Additional consideration payable related to acquisitions		11.1	0.0	3.9
Acquisition of businesses:
Assets acquired		141.6	0.0	6.5
Liabilities acquired		(84.1)	0.0	(4.1)
Total net assets acquired		57.5	0.0	2.4
Cash and cash equivalents		1,108.3	1,108.5	1,109.6
Cash segregated under federal and other regulations	[1]	2,420.5	2,461.6	2,260.3
Securities segregated under federal and other regulations	[1]	0.0	200.0	0.0
Cash segregated and deposited with or pledged to exchange-clearing organizations and other futures commission merchants (“FCMs”)	[2]	1,256.5	2,138.2	2,739.6
Securities segregated and pledged to exchange-clearing organizations	[2]	1,256.4	376.8	400.0
Total cash, segregated cash, cash equivalents, and segregated cash equivalents shown in the consolidated statements of cash flows		6,041.7	6,285.1	6,509.5
Non cash equivalent segregated assets		5.8	605.6	14.1
Non segregated cash and other non cash equivalent assets included with in deposits and receivables from broker dealers clearing organizations and counter parties		$ 4,930.9	$ 4,327.6	$ 2,153.3

[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 $5.8 million, $605.6 million, and $14.1 million as of September 30, 2023, 2022, and 2021, 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 $4,930.9 million, $4,327.6 million, and $2,153.3 million as of September 30, 2023, 2022, and 2021, respectively, included within Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net on the Consolidated Balance Sheets.