Consolidated Statements of Cash Flows - USD ($) $ in Millions		12 Months Ended
		Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Cash flows from operating activities:
Net income		$ 207.1	$ 116.3	$ 169.6
Adjustments to reconcile net income to net cash (used in)/provided by operating activities:
Depreciation and amortization		44.4	36.5	19.7
Amortization of operating right of use assets		15.9	12.2	9.9
Provision for bad debts, net of recoveries and impairment		15.8	10.4	18.7
Deferred income taxes		(0.3)	3.2	4.1
Amortization and extinguishment of debt issuance costs		4.5	3.9	6.5
Actuarial gain on pension and postretirement benefits		(0.1)	(0.3)	(0.2)
Amortization of share-based compensation expense		17.8	13.9	10.3
Gain on acquisition		0.0	(3.3)	(81.9)
Gain on stock sales of clearing organization memberships		0.0	(0.7)	0.0
Changes in operating assets and liabilities, net:
Securities and other assets segregated under federal and other regulations		(591.5)	(1.0)	293.0
Securities purchased under agreements to resell		567.9	(543.7)	(271.7)
Securities borrowed		953.3	(723.1)	(16.8)
Deposits with and receivables from broker-dealers, clearing organizations, and counterparties		(2,174.3)	(132.0)	(326.0)
Receivable from clients, net		(119.7)	(68.3)	0.9
Notes receivable, net		1.0	(4.4)	1.2
Income taxes receivable		10.4	(9.6)	(11.1)
Financial instruments owned, at fair value		187.3	(1,626.9)	(552.5)
Physical commodities inventory		(67.2)	(166.4)	(51.8)
Other assets		(9.8)	(16.7)	(3.7)
Accounts payable and other accrued liabilities		101.4	35.7	42.7
Operating lease liabilities		(16.0)	(8.6)	(9.5)
Payable to clients		2,055.1	2,146.7	2,093.7
Payable to broker-dealers, clearing organizations and counterparties		46.3	76.0	270.8
Income taxes payable		2.8	(9.4)	(0.3)
Securities sold under agreements to repurchase		(1,145.3)	1,185.4	381.8
Securities loaned		(964.1)	711.7	(18.0)
Financial instruments sold, not yet purchased, at fair value		627.8	1,085.2	(28.8)
Net cash (used in)/provided by operating activities		(229.5)	2,122.7	1,950.6
Cash flows from investing activities:
Proceeds from stock sales of clearing organization memberships		0.2	1.6	0.0
Cash paid for acquisitions		(0.2)	(2.4)	(225.0)
Sale of property and equipment		0.0	3.1	0.0
Purchase of property and equipment and internally developed software		(49.5)	(62.1)	(16.6)
Net cash used in investing activities		(49.5)	(59.8)	(241.6)
Cash flows from financing activities:
Net change in lenders under loans with maturities 90 days or less		211.5	(33.5)	99.7
Proceeds from lenders under loans with maturities greater than 90 days		547.0	191.4	608.5
Repayments of lenders under loans with maturities greater than 90 days		(522.0)	(186.4)	(642.0)
Proceeds from issuance of senior secured term loan		0.0	0.0	21.5
Repayments of senior secured term loan		(170.3)	(9.8)	(9.8)
Proceeds from issuance of senior secured notes		0.0	0.0	344.8
Repayment of senior secured notes		(0.5)	(1.6)	(92.1)
Issuance of note payable		0.0	9.0	0.0
Repayments of note payable		0.0	0.0	(0.4)
Deferred payments on acquisitions		(3.0)	(2.2)	(0.9)
Payment of contingent consideration		(3.6)	0.0	0.0
Share repurchase		0.0	(11.7)	(7.5)
Debt issuance costs		0.0	0.0	(15.0)
Exercise of stock options		6.7	9.2	5.5
Net cash provided by/(used in) financing activities		65.8	(35.6)	312.3
Effect of exchange rates on cash, segregated cash, cash equivalents, and segregated cash equivalents		(11.2)	13.8	(4.2)
Net (decrease) increase in cash, segregated cash, cash equivalents, and segregated cash equivalents		(224.4)	2,041.1	2,017.1
Cash, segregated cash, cash equivalents, and segregated cash equivalents at beginning of period		6,509.5	4,468.4	2,451.3
Cash, segregated cash, cash equivalents, and segregated cash equivalents at end of period		6,285.1	6,509.5	4,468.4
Supplemental disclosure of cash flow information:
Cash paid for interest		149.2	87.0	90.4
Income taxes paid, net of cash refunds		56.3	52.0	44.0
Supplemental disclosure of non-cash investing and financing activities:
Identified intangible assets and goodwill on acquisitions		0.2	6.5	11.8
Additional consideration payable related to acquisitions		0.0	3.9	21.6
Acquisition of businesses:
Assets acquired		0.0	6.5	1,169.2
Liabilities acquired		0.0	(4.1)	(359.5)
Total net assets acquired		0.0	2.4	809.7
Cash and cash equivalents		1,108.5	1,109.6	952.6
Cash segregated under federal and other regulations	[1]	2,461.6	2,260.3	1,907.2
Securities segregated under federal and other regulations	[1]	200.0	0.0	0.0
Cash segregated and deposited with or pledged to exchange-clearing organizations and other futures commission merchants (“FCMs”)	[2]	2,138.2	2,739.6	698.7
Securities segregated and pledged to exchange-clearing organizations	[2]	376.8	400.0	909.9
Total cash, segregated cash, cash equivalents, and segregated cash equivalents shown in the consolidated statements of cash flows		6,285.1	6,509.5	4,468.4
Non cash equivalent segregated assets		605.6	14.1	13.0
Non segregated cash and other non cash equivalent assets included with in deposits and receivables from broker dealers clearing organizations and counter parties		$ 4,327.6	$ 2,153.3	$ 2,021.3

[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 $605.6 million, $14.1 million, and $13.0 million as of September 30, 2022, 2021, and 2020, 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 $4,327.6 million, $2,153.3 million, and $2,021.3 million as of September 30, 2022, 2021, and 2020, respectively, included within Deposits with and receivables from broker-dealers, clearing organizations, and counterparties, net on the Consolidated Balance Sheets.