Fair value measurements - Assets and Liabilities Measured at Fair Value on Recurring Basis (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020
ASSETS
Deposits with clearing organizations	$ 29,083	$ 23,991
Securities owned
Securities owned, at fair value	634,504	610,517
Investments	5,521	4,836
Derivative contracts
Derivative contracts, total		15
Total	676,649	638,704
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	71,958	126,171
Derivative contracts:
Derivative contracts	368	220
Total	72,326	126,391
Equity Securities
Securities owned
Securities owned, at fair value	45,380	36,554
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	18,679
Money markets
Securities owned
Securities owned, at fair value	31	200
Auction rate securities
Securities owned
Securities owned, at fair value	31,804	30,701
Corporate equities
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		17,892
U.S. Treasury securities
Securities owned
Securities owned, at fair value	505,875	448,312
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	42,298	93,261
U.S. Agency securities
Securities owned
Securities owned, at fair value	5,622	24,616
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	4	9
Sovereign obligations
Securities owned
Securities owned, at fair value	1,494	367
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		623
Corporate debt and other obligations
Securities owned
Securities owned, at fair value	8,111	23,977
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	2,515	5,283
Mortgage and other asset-backed securities
Securities owned
Securities owned, at fair value	3,889	3,103
Municipal obligations
Securities owned
Securities owned, at fair value	18,520	25,190
Convertible bonds
Securities owned
Securities owned, at fair value	13,778	17,497
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	8,462	9,103
Other Investments
Securities owned
Investments	12,970	4,181
Level 1
ASSETS
Deposits with clearing organizations	29,083	23,991
Securities owned
Securities owned, at fair value	551,286	485,066
Derivative contracts
Derivative contracts, total		0
Total	580,369	509,057
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	60,977	111,153
Derivative contracts:
Derivative contracts	287	22
Total	61,264	111,175
Level 1 | Equity Securities
Securities owned
Securities owned, at fair value	45,380	36,554
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	18,679
Level 1 | Money markets
Securities owned
Securities owned, at fair value	31	200
Level 1 | Auction rate securities
Securities owned
Securities owned, at fair value	0
Level 1 | Corporate equities
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		17,892
Level 1 | U.S. Treasury securities
Securities owned
Securities owned, at fair value	505,875	448,312
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	42,298	93,261
Level 1 | U.S. Agency securities
Securities owned
Securities owned, at fair value	0	0
Level 2
ASSETS
Deposits with clearing organizations	0
Securities owned
Securities owned, at fair value	51,414	94,750
Derivative contracts
Derivative contracts, total		15
Total	64,476	98,946
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	10,981	15,018
Derivative contracts:
Derivative contracts	81	3
Total	11,062	15,021
Level 2 | Auction rate securities
Securities owned
Securities owned, at fair value	0	0
Level 2 | U.S. Agency securities
Securities owned
Securities owned, at fair value	5,622	24,616
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	4	9
Level 2 | Sovereign obligations
Securities owned
Securities owned, at fair value	1,494	367
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		623
Level 2 | Corporate debt and other obligations
Securities owned
Securities owned, at fair value	8,111	23,977
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	2,515	5,283
Level 2 | Mortgage and other asset-backed securities
Securities owned
Securities owned, at fair value	3,889	3,103
Level 2 | Municipal obligations
Securities owned
Securities owned, at fair value	18,520	25,190
Level 2 | Convertible bonds
Securities owned
Securities owned, at fair value	13,778	17,497
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	8,462	9,103
Level 2 | Other Investments
Securities owned
Investments	12,970	4,181
Level 3
ASSETS
Deposits with clearing organizations	0
Securities owned
Securities owned, at fair value	31,804	30,701
Derivative contracts
Derivative contracts, total		0
Total	31,804	30,701
Derivative contracts:
Derivative contracts	0	195
Total	0	195
Level 3 | Auction rate securities
Securities owned
Securities owned, at fair value	31,804	30,701
Level 3 | Municipal obligations
Securities owned
Securities owned, at fair value	0	0
TBAs
Derivative contracts
Derivative contracts, total	92	15
Derivative contracts:
Derivative contracts	81	3
TBAs | Level 2
Derivative contracts
Derivative contracts, total	92	15
Derivative contracts:
Derivative contracts	81	3
Futures
Derivative contracts:
Derivative contracts	287	22
Futures | Level 1
Derivative contracts:
Derivative contracts	$ 287	22
ARS purchase commitments
Derivative contracts:
Derivative contracts		195
ARS purchase commitments | Level 2
Derivative contracts:
Derivative contracts		0
ARS purchase commitments | Level 3
Derivative contracts:
Derivative contracts		$ 195