Description of Business and Significant Accounting Policies (Details) $ / shares in Units, $ in Millions	12 Months Ended
	Sep. 30, 2020 USD ($) country client $ / shares shares	Sep. 30, 2019 USD ($) $ / shares shares	Sep. 30, 2018 USD ($)	Jan. 14, 2019
Number of commercial and institutional clients (more than) | client	32,000
Number retail clients (more than) | client	330,000
Number of countries in which entity operates (more than) | country	180
Selling and marketing	$ 12.2	$ 5.2	$ 6.2
Amount recognized in loss due to inflationary accounting		3.9	3.4
Net assets and liabilities denominated in argentine pesos	0.1	(5.5)
Cash denominated in argentine pesos	0.1	1.4
Net denominated in argentine pesos	0.9	1.0
Cash held at banks and money market funds - segregated	1,907.2	743.9
US government obligations and other securities	10.6	299.8
Commodities warehouse receipts	2.4	6.2
Cash and cash equivalents - deposits and receivables	1,600.0	1,600.0
US government securities and other securities - deposits and receivables	$ 1,949.3	603.8
Acquired finite-lived intangible asset, weighted average useful life	1 year
Fair Value of exchange memberships	$ 6.7	$ 6.0
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
Cumulative effect of new accounting principle in period of adoption		$ 0.7
Minimum [Member]
Property plant and equipment, useful life	3 years
Identifiable intangible assets	5 years
Maximum [Member]
Property plant and equipment, useful life	10 years
Identifiable intangible assets	20 years
Retail [Member]
Number of countries in which entity operates (more than) | country	130
Software Development [Member]
Property plant and equipment, useful life	3 years
Exchange Memberships Representing an Ownership Interest [Member]
Memberships in exchanges owned	$ 5.6	5.6
Exchange Memberships not Representing an Ownership Interest [Member]
Memberships in exchanges owned	$ 5.8	$ 5.8
Commission and Clearing Fees [Member]
Prior period reclassification adjustment			$ 35.0
GMP Securities Acquisition [Member]
Percentage of stock purchased				100.00%