Description of Business and Significant Accounting Policies (Details)		12 Months Ended
	Oct. 01, 2020 USD ($)	Sep. 30, 2021 USD ($) country client $ / shares shares	Sep. 30, 2020 USD ($) $ / shares shares	Sep. 30, 2019 USD ($)
Number of countries in which entity operates (more than) | country		180
Number of commercial and institutional clients (more than) | client		45,000
Number retail clients (more than) | client		370,000
Selling and marketing		$ 33,300,000	$ 12,200,000	$ 5,200,000
Translation losses		(800,000)
Net assets denominated in argentine pesos		400,000
Net liabilities denominated in argentine pesos			100,000
Cash denominated in argentine pesos (less than)		100,000	100,000
Net nonmonetary denominated in Argentine pesos		900,000	900,000
Cash held at banks and money market funds - segregated		2,260,300,000	1,907,200,000
US government obligations and other securities		200,000	10,600,000
Commodities warehouse receipts		13,900,000	2,400,000
Cash and cash equivalents - deposits and receivables		3,100,000,000	1,600,000,000
US government securities and other securities - deposits and receivables		$ 810,700,000	1,949,300,000
Acquired finite-lived intangible asset, weighted average useful life		1 year
Goodwill impairment charges		$ 0	0	0
Fair Value of exchange memberships		$ 6,800,000	$ 6,700,000
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
Retained earnings		$ 682,500,000	$ 572,400,000
Income tax expense		37,800,000	37,100,000	25,900,000
Other expense | Revision of Prior Period, Adjustment
Selling and marketing				(5,200,000)
Selling and marketing expense | Revision of Prior Period, Adjustment
Selling and marketing				5,200,000
Cumulative Effect, Period of Adoption, 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	5,600,000
Exchange Memberships not Representing an Ownership Interest
Memberships in exchanges owned		$ 6,000,000	$ 5,800,000
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 losses				$ 3,900,000
Geographic Concentration Risk | Revenue Benchmark | ARGENTINA
Percentage of operating revenues		1.00%
Retail
Number of countries in which entity operates (more than) | country		180