Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 142.4	$ 108.5
Principal gains, net	203.4	112.5
Interest income	21.2	46.0
Total revenues	9,250.5	11,245.0
United States
Disaggregation of Revenue [Line Items]
Total revenues	758.9	512.3
Europe
Disaggregation of Revenue [Line Items]
Total revenues	172.4	111.6
South America
Disaggregation of Revenue [Line Items]
Total revenues	14.6	15.2
Middle East and Asia
Disaggregation of Revenue [Line Items]
Total revenues	8,302.0	10,605.5
Other
Disaggregation of Revenue [Line Items]
Total revenues	2.6	0.4
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	119.7	84.6
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	22.7	23.9
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	46.3	32.4
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.8	5.5
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	14.4	4.3
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.2	1.3
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.3	2.1
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.2	0.3
Sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	68.2	45.9
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.3	3.1
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.9	3.7
Trailing commissions
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	7.2	6.8
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	38.5	29.5
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.1	1.5
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.4	3.5
Commission and clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	119.4	87.2
Underwriting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.2	0.2
Asset management fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	8.7	7.5
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	6.0	5.6
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.8	4.0
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.1	3.0
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.2	1.0
Consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	23.0	21.3
Physical precious metals trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	8,408.9	10,658.0
Physical agricultural and energy product trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 474.6	$ 320.0