Description of Business and Significant Accounting Policies (Details)		12 Months Ended
	Oct. 01, 2020 USD ($)	Sep. 30, 2023 USD ($) client country $ / shares shares	Sep. 30, 2022 USD ($) $ / shares shares	Sep. 30, 2021 USD ($)	Sep. 30, 2020
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				$ 0
Net liabilities denominated in argentine pesos		$ 200,000
Net assets denominated in argentine pesos			$ 400,000
Cash denominated in argentine pesos (less than)		800,000	100,000
Net nonmonetary denominated in Argentine pesos		700,000	1,100,000
Cash held at banks and money market funds - segregated		2,420,500,000	2,461,600,000
US government obligations and other securities		0	786,000,000
Commodities warehouse receipts		5,800,000	19,700,000
Cash and cash equivalents - deposits and receivables		2,512,900,000	2,515,000,000
US government securities and other securities - deposits and receivables		$ 4,041,600,000	4,272,900,000
Acquired finite-lived intangible asset, weighted average useful life		1 year
Goodwill impairment charges		$ 0	0	0
Intangible assets impairment charges		$ 0	$ 0	0
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]
Retained earnings		$ 1,128,100,000	$ 889,600,000
Income tax expense		$ 84,500,000	70,100,000	$ 37,800,000
Cumulative transition adjustment
Retained earnings	$ 6,200,000
Income tax expense	$ 2,000,000
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		$ 6,600,000	$ 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