Allowance for Doubtful Accounts - Narrative (Details) - USD ($)	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Accounts, Notes, Loans and Financing Receivable [Line Items]
Allowance for doubtful accounts - deposits with and receivables from broker-dealers, clearings organizations, and counterparties	$ 1,300,000	$ 1,300,000
Allowance for doubtful accounts receivable	38,500,000	25,800,000
Allowance for doubtful accounts	0	0
Accounts receivable, allowance for doubtful accounts	5,900,000	35,600,000	$ 300,000
Provision for bad debts, net of recoveries and impairment	10,400,000	13,000,000	2,500,000
Bad debt expense (recovery)	0	0	(12,400,000)
Net increase in provision for bad debts			2,600,000
Allowance for doubtful accounts receivable, recoveries			400,000
Commerical Segment
Accounts, Notes, Loans and Financing Receivable [Line Items]
Provision for bad debts, net of recoveries and impairment	8,500,000	3,500,000
Bad debt expense (recovery)	4,600,000	3,200,000
Net increase in provision for bad debts			2,700,000
Institutional Segment
Accounts, Notes, Loans and Financing Receivable [Line Items]
Provision for bad debts, net of recoveries and impairment	600,000	5,400,000
Net increase in provision for bad debts			$ 1,400,000
Global Payments
Accounts, Notes, Loans and Financing Receivable [Line Items]
Provision for bad debts, net of recoveries and impairment	200,000
Retail
Accounts, Notes, Loans and Financing Receivable [Line Items]
Provision for bad debts, net of recoveries and impairment	$ 1,100,000	$ 600,000