Revenue from Contracts with Clients - Revenue from Contracts with Clients (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	$ 2,119.5	$ 487.3	$ 452.0
Sales of physical commodities	40,961.6	52,899.2	31,830.3
Principal gains, net	892.0	622.2	415.8
Interest income	102.4	130.9	198.9
Total revenues	42,534.2	54,139.6	32,897.0
Point-in-time
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2,021.8	396.1	362.7
Time elapsed
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	97.7	91.2	89.3
Exchange-traded futures and options
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	190.6	143.7	144.9
OTC derivative brokerage
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	15.9	19.7	32.1
Equities and fixed income
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	60.5	39.9	16.1
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	5.5	5.2	7.5
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	9.7	8.4	7.3
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	2.3	1.4	1.3
Total sales-based commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	284.5	218.3	209.2
Mutual funds
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	14.5	12.9	12.4
Insurance and annuity products
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	17.0	15.3	14.4
Total trailing commission
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	31.5	28.2	26.8
Clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	150.9	139.0	118.8
Trade conversion fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	11.2	8.9	7.5
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	9.1	9.2	10.1
Total commission and clearing fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	487.2	403.6	372.4
Underwriting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	0.6	0.6	0.7
Asset management fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	38.3	31.3	26.2
Advisory and consulting fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	24.9	22.2	20.0
Sweep program fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	3.0	9.5	16.3
Client account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	15.8	12.3	10.6
Other
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	8.4	7.8	5.8
Total consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	91.0	83.7	79.6
Precious metals retail sales
Disaggregation of Revenue [Line Items]
Revenue from contract with customer	1,541.3	0.0	0.0
Physical precious metals trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	37,250.4	51,598.5	30,694.5
Physical agricultural and energy product trading
Disaggregation of Revenue [Line Items]
Sales of physical commodities	$ 2,169.9	$ 1,300.7	$ 1,135.8