Revenues from contracts with customers (Details) - USD ($)	3 Months Ended								12 Months Ended
	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2017	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017
Disaggregation of Revenue [Line Items]
Total revenues	$ 11,279,600,000	$ 7,873,000,000	$ 7,192,200,000	$ 6,552,200,000	$ 6,078,800,000	$ 7,118,300,000	$ 6,507,000,000	$ 7,918,600,000	$ 32,897,000,000	$ 27,622,700,000	$ 29,423,600,000
Commission and clearing fees									372,400,000	391,800,000	318,600,000
Consulting, management, and account fees									79,600,000	71,100,000	65,000,000
Revenue from Contract with Customer, Including Assessed Tax									452,000,000	462,900,000	383,600,000
Sales of physical commodities									31,830,300,000	26,682,400,000	28,673,300,000
Principal gains, net									415,800,000	354,100,000	297,000,000
Interest income									198,900,000	123,300,000	69,700,000
Transferred at Point in Time [Member]
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer, Including Assessed Tax									362,700,000	379,700,000	306,900,000
Transferred over Time [Member]
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer, Including Assessed Tax									89,300,000	83,200,000	76,700,000
Commission and Clearing Fees
Disaggregation of Revenue [Line Items]
Commission and clearing fees									372,400,000	391,800,000	318,600,000
Trailing Commissions [Domain]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									26,800,000	27,800,000	27,300,000
Trailing Commissions [Domain] | Variable Annuity [Member]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									14,400,000	14,600,000	14,200,000
Trailing Commissions [Domain] | Mutual Fund Trailing Commissions [Member]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									12,400,000	13,200,000	13,100,000
Clearing Fees [Domain]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									118,800,000	123,300,000	88,500,000
Trade Conversion Fees [Domain]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									7,500,000	6,800,000	0
Other Commissions [Domain]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									10,100,000	15,100,000	12,900,000
Consulting, management, and account fees [Domain] | Underwriting Fees [Member]
Disaggregation of Revenue [Line Items]
Consulting, management, and account fees									700,000	1,700,000	2,300,000
Consulting, management, and account fees [Domain] | Asset Management [Member]
Disaggregation of Revenue [Line Items]
Consulting, management, and account fees									26,200,000	24,800,000	25,700,000
Consulting, management, and account fees [Domain] | Advisory and Consulting Fees [Member]
Disaggregation of Revenue [Line Items]
Consulting, management, and account fees									20,000,000	19,000,000	17,700,000
Consulting, management, and account fees [Domain] | Sweep Program Fees [Member]
Disaggregation of Revenue [Line Items]
Consulting, management, and account fees									16,300,000.0	11,600,000.0	6,000,000.0
Consulting, management, and account fees [Domain] | Client Account Fees [Member]
Disaggregation of Revenue [Line Items]
Consulting, management, and account fees									10,600,000.0	11,100,000.0	10,800,000.0
Consulting, management, and account fees [Domain] | Other Consulting, Management, and Account Fees [Member]
Disaggregation of Revenue [Line Items]
Consulting, management, and account fees									5,800,000.0	2,900,000.0	2,500,000.0
Consulting, management, and account fees
Disaggregation of Revenue [Line Items]
Consulting, management, and account fees									79,600,000.0	71,100,000.0	65,000,000.0
Sales [Member] | Precious Metals Trading Revenues [Member]
Disaggregation of Revenue [Line Items]
Sales of physical commodities									30,694,500,000	25,762,900,000	28,018,400,000
Sales [Member] | Physical Commodity Origination and Merchandising [Member]
Disaggregation of Revenue [Line Items]
Sales of physical commodities									1,135,800,000	919,500,000	654,900,000
Principal gains, net
Disaggregation of Revenue [Line Items]
Principal gains, net									415,800,000	354,100,000	297,000,000
Interest Income
Disaggregation of Revenue [Line Items]
Interest income									198,900,000	123,300,000	69,700,000
Sales Based Commissions [Domain]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									209,200,000	218,800,000	189,900,000
Sales Based Commissions [Domain] | Exhange-Traded Futures and Options [Member]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									144,900,000	163,400,000	129,700,000
Sales Based Commissions [Domain] | OTC Derivative Brokerage [Member]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									32,100,000	30,300,000	28,300,000
Sales Based Commissions [Domain] | Equities and Fixed Income Commissions [Member]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									16,100,000	11,200,000	16,000,000
Sales Based Commissions [Domain] | Mutual Fund Sales Based Commissions [Member]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									7,500,000	7,200,000	7,900,000
Sales Based Commissions [Domain] | Variable Annuity [Member]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									7,300,000	5,800,000	6,000,000
Sales Based Commissions [Domain] | Other Sales Based Commissions [Member]
Disaggregation of Revenue [Line Items]
Commission and clearing fees									$ 1,300,000	$ 900,000	$ 2,000,000