Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2023	Mar. 31, 2022	Mar. 31, 2023	Mar. 31, 2022
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 917.8	$ 970.8	$ 1,864.2	$ 1,891.5
Principal gains, net	256.6	323.5	510.8	574.6
Interest income	226.8	31.2	423.0	62.2
Revenues	16,161.0	16,382.7	29,172.6	30,724.1
Total operating revenues	704.4	544.7	1,359.2	995.2
United States
Disaggregation of Revenue [Line Items]
Revenues	1,471.1	1,204.6	3,034.7	2,329.3
Total operating revenues	538.5	364.5	1,028.4	668.6
Europe
Disaggregation of Revenue [Line Items]
Revenues	912.0	933.6	1,827.0	1,818.2
Total operating revenues	105.5	131.3	207.0	239.0
South America
Disaggregation of Revenue [Line Items]
Revenues	56.5	23.6	118.7	41.3
Total operating revenues	32.0	23.6	63.5	41.3
Middle East and Asia
Disaggregation of Revenue [Line Items]
Revenues	13,720.0	14,218.5	24,186.3	26,530.7
Total operating revenues	27.1	23.0	54.5	41.8
Other
Disaggregation of Revenue [Line Items]
Revenues	1.4	2.4	5.9	4.6
Total operating revenues	1.3	2.3	5.8	4.5
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	878.2	943.6	1,787.3	1,837.4
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	39.6	27.2	76.9	54.1
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	55.3	57.7	104.0	102.3
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	4.5	4.9	8.1	9.3
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	15.6	17.1	31.0	31.7
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.9	1.2	1.5	2.4
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.7	2.4	4.5	5.2
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1.1	0.9	2.2	1.7
Total sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	80.1	84.2	151.3	152.6
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.1	3.6	6.1	7.5
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.5	4.2	7.0	8.6
Total trailing commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	6.6	7.8	13.1	16.1
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	40.0	40.6	76.0	77.0
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.0	4.0	4.4	6.0
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.0	1.8	3.9	3.0
Total commission and clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	130.7	138.4	248.7	254.7
Revenues	130.7	138.4	248.7	254.7
Underwriting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.1	0.1	0.3	0.3
Asset management fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	11.1	11.4	21.8	22.0
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	9.0	7.5	17.7	15.0
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	12.9	0.5	24.3	1.0
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.7	4.3	7.5	8.0
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.9	1.6	8.9	3.2
Total consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	40.7	25.4	80.5	49.5
Revenues	40.7	25.4	80.5	49.5
Precious metals sales
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	746.4	807.0	1,535.0	1,587.3
Physical precious metals trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	13,703.1	14,211.3	24,182.1	26,526.6
Physical agricultural and energy product trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 1,056.7	$ 845.9	$ 2,192.5	$ 1,669.2
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	5.70%	5.90%	6.40%	6.20%