Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2022	Dec. 31, 2021
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 946.4	$ 920.7
Principal gains, net	254.2	251.1
Interest income	196.2	31.0
Revenues	13,011.6	14,341.4
Total operating revenues	654.8	450.5
United States
Disaggregation of Revenue [Line Items]
Revenues	1,563.6	1,124.7
Total operating revenues	489.9	304.1
Europe
Disaggregation of Revenue [Line Items]
Revenues	915.0	884.6
Total operating revenues	101.5	107.7
South America
Disaggregation of Revenue [Line Items]
Revenues	62.2	17.7
Total operating revenues	31.5	17.7
Middle East and Asia
Disaggregation of Revenue [Line Items]
Revenues	10,466.3	12,312.2
Total operating revenues	27.4	18.8
Other
Disaggregation of Revenue [Line Items]
Revenues	4.5	2.2
Total operating revenues	4.5	2.2
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	909.1	893.8
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	37.3	26.9
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	48.7	44.6
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.6	4.4
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	15.4	14.6
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.6	1.2
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.8	2.8
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.1	0.8
Total sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	71.2	68.4
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.0	3.9
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.5	4.4
Total trailing commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	6.5	8.3
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	36.0	36.4
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.4	2.0
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.9	1.2
Total commission and clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	118.0	116.3
Revenues	118.0	116.3
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	10.7	10.6
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	8.7	7.5
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	11.4	0.5
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.8	3.7
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	5.0	1.6
Total consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	39.8	24.1
Revenues	39.8	24.1
Precious metals sales
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	788.6	780.3
Physical precious metals trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	10,479.0	12,315.3
Physical agricultural and energy product trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 1,135.8	$ 823.3