Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2023	Dec. 31, 2022
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 627.4	$ 946.4
Principal gains, net	293.8	254.2
Interest income	290.1	196.2
Revenues	19,573.0	13,011.6
Total operating revenues	784.2	654.8
United States
Disaggregation of Revenue [Line Items]
Revenues	1,603.5	1,563.6
Total operating revenues	568.0	489.9
Europe
Disaggregation of Revenue [Line Items]
Revenues	658.4	915.0
Total operating revenues	135.6	101.5
South America
Disaggregation of Revenue [Line Items]
Revenues	128.0	62.2
Total operating revenues	41.2	31.5
Middle East and Asia
Disaggregation of Revenue [Line Items]
Revenues	17,175.6	10,466.3
Total operating revenues	32.0	27.4
Other
Disaggregation of Revenue [Line Items]
Revenues	7.5	4.5
Total operating revenues	7.4	4.5
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	589.7	909.1
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	37.7	37.3
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	51.4	48.7
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.8	3.6
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	16.5	15.4
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.7	0.6
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.0	1.8
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	(0.1)	1.1
Total sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	73.3	71.2
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.0	3.0
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.7	3.5
Total trailing commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	6.7	6.5
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	43.3	36.0
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.0	2.4
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.4	1.9
Total commission and clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	129.7	118.0
Revenues	129.7	118.0
Underwriting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.0	0.2
Asset management fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	11.4	10.7
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	8.2	8.7
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	11.4	11.4
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.2	3.8
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.3	5.0
Total consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	38.5	39.8
Revenues	38.5	39.8
Precious metals sales under ASC Topic 606
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	459.2	788.6
Physical precious metals under ASC Topic 815
Disaggregation of Revenue [Line Items]
Sales of physical commodities	17,162.5	10,479.0
Physical agricultural and energy products
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 1,199.2	$ 1,135.8
Revenue from Contract with Customer Benchmark | Customer Concentration Risk | Clients
Disaggregation of Revenue [Line Items]
Revenues from contracts with clients as a percentage of total revenues	3.20%	7.30%