Description of Business and Significant Accounting Policies (Details)		12 Months Ended
	Oct. 01, 2020 USD ($)	Sep. 30, 2022 USD ($) client country $ / shares shares	Sep. 30, 2021 USD ($) $ / shares shares	Sep. 30, 2020 USD ($)	Sep. 30, 2019	Sep. 30, 2018
Number of countries in which entity operates (more than) | country		180
Number of commercial, institutional and global payment clients (more than) | client		54,000
Number retail clients (more than) | client		400,000
Translation gains			$ 800,000	$ 0
Net liabilities denominated in argentine pesos		$ 400,000
Net assets denominated in argentine pesos			400,000
Cash denominated in argentine pesos (less than)		100,000	100,000
Net nonmonetary denominated in Argentine pesos		1,100,000	900,000
Cash held at banks and money market funds - segregated		2,461,600,000	2,260,300,000
US government obligations and other securities		786,000,000	200,000
Commodities warehouse receipts		19,700,000	13,900,000
Cash and cash equivalents - deposits and receivables		2,515,000,000	3,139,600,000
US government securities and other securities - deposits and receivables		$ 4,272,900,000	810,700,000
Acquired finite-lived intangible asset, weighted average useful life		1 year
Goodwill impairment charges		$ 0	0	$ 0
Fair Value of exchange memberships		$ 6,200,000	$ 6,800,000
Preferred stock - authorized (in shares) | shares		1,000,000	1,000,000
Preferred stock - par value (in dollar per share) | $ / shares		$ 0.01	$ 0.01
Preferred stock - outstanding (in shares) | shares		0	0
Accounting Standards Update [Extensible Enumeration]				Accounting Standards Update 2016-13 [Member]	Accounting Standards Update 2018-02 [Member]	Accounting Standards Update 2018-02 [Member]
Retained earnings		$ 889,600,000	$ 682,500,000
Income tax expense		70,100,000	37,800,000	$ 37,100,000
Cumulative transition adjustment
Retained earnings	$ (6,200,000)
Income tax expense	$ 2,000,000
Exchange Memberships Representing an Ownership Interest
Memberships in exchanges owned		5,500,000	5,500,000
Exchange Memberships not Representing an Ownership Interest
Memberships in exchanges owned		$ 5,800,000	$ 6,000,000
Minimum
Property plant and equipment, useful life		3 years
Identifiable intangible assets		5 years
Maximum
Property plant and equipment, useful life		10 years
Identifiable intangible assets		20 years
Capitalized software development
Property plant and equipment, useful life		3 years
Argentina
Translation gains		$ 2,100,000
Argentina | Revenue Benchmark | Geographic Concentration Risk
Percentage of operating revenues		1.00%
Retail
Number of countries in which entity operates (more than) | country		180