Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2022	Mar. 31, 2021	Mar. 31, 2022	Mar. 31, 2021
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 970.8	$ 563.1	$ 1,891.5	$ 818.6
Principal gains, net	323.5	265.2	574.6	468.6
Interest income	31.2	23.4	62.2	44.6
Revenues	16,382.7	11,244.8	30,724.1	20,495.3
Total operating revenues	544.7	471.4	995.2	851.5
United States
Disaggregation of Revenue [Line Items]
Revenues	1,204.6	853.6	2,329.3	1,612.5
Total operating revenues	364.5	349.7	668.6	635.9
Europe
Disaggregation of Revenue [Line Items]
Revenues	933.6	490.1	1,818.2	662.5
Total operating revenues	131.3	87.1	239.0	147.6
South America
Disaggregation of Revenue [Line Items]
Revenues	23.6	14.5	41.3	29.1
Total operating revenues	23.6	14.5	41.3	29.1
Middle East and Asia
Disaggregation of Revenue [Line Items]
Revenues	14,218.5	9,885.1	26,530.7	18,187.1
Total operating revenues	23.0	18.6	41.8	34.8
Other
Disaggregation of Revenue [Line Items]
Revenues	2.4	1.5	4.6	4.1
Total operating revenues	2.3	1.5	4.5	4.1
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	943.6	538.6	1,837.4	771.4
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	27.2	24.5	54.1	47.2
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	57.7	49.4	102.3	95.7
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.9	4.6	9.3	8.4
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	17.1	19.4	31.7	33.8
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.2	1.5	2.4	2.7
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.4	2.3	5.2	4.6
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.9	0.1	1.7	0.3
Total sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	84.2	77.3	152.6	145.5
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.6	3.6	7.5	6.9
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.2	4.2	8.6	8.1
Total trailing commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	7.8	7.8	16.1	15.0
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	40.6	39.4	77.0	77.9
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.0	3.6	6.0	5.7
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.8	1.7	3.0	5.1
Total commission and clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	138.4	129.8	254.7	249.2
Underwriting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.1	0.2	0.3	0.4
Asset management fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	11.4	9.3	22.0	18.0
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	7.5	6.6	15.0	12.6
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.5	0.8	1.0	1.6
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.3	3.8	8.0	7.9
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.6	1.4	3.2	4.6
Total consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	25.4	22.1	49.5	45.1
Precious metals sales
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	807.0	411.2	1,587.3	524.3
Physical precious metals trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	14,211.3	9,884.5	26,526.6	18,180.3
Physical agricultural and energy product trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 845.9	$ 508.6	$ 1,669.2	$ 983.2