Fair value measurements - Assets and Liabilities Measured at Fair Value on Recurring Basis (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021
ASSETS
Deposits with clearing organizations	$ 24,937	$ 29,083
Securities owned
Securities owned, at fair value	498,594	634,504	[1]
Securities owned and sold, fair value	498,594	634,504
Investments	7,068	12,970
Derivative contracts:
Total	532,361	676,649
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	52,768	71,958	[1]
Derivative contracts:
Derivative contracts	$ 1,805	368
Derivative Liability, Statement of Financial Position [Extensible Enumeration]	Accounts payable and other liabilities
Total	$ 54,573	72,326
Money markets
Securities owned
Securities owned, at fair value	0	31
Auction rate securities
Securities owned
Securities owned, at fair value	31,776	31,804
TBAs
Derivative contracts:
Derivative contracts, total	1,762	92
Derivative contracts:
Derivative contracts	1,761	81
Futures
Derivative contracts:
Derivative contracts	44	287
U.S. Treasury securities
Securities owned
Securities owned, at fair value	362,815	505,875
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	25,006	42,298
U.S. Agency securities
Securities owned
Securities owned, at fair value	6,012	5,622
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	3	4
Sovereign obligations
Securities owned
Securities owned, at fair value	9,502	1,494
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	9,048
Corporate debt and other obligations
Securities owned
Securities owned, at fair value	9,844	8,111
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	2,905	2,515
Mortgage and other asset-backed securities
Securities owned
Securities owned, at fair value	1,882	3,889
Municipal obligations
Securities owned
Securities owned, at fair value	30,126	18,520
Convertible bonds
Securities owned
Securities owned, at fair value	21,800	13,778
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	4,428	8,462
Corporate equities | Corporate equities
Securities owned
Securities owned, at fair value	24,837	45,380
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	11,378	18,679
Level 1
ASSETS
Deposits with clearing organizations	24,937	29,083
Securities owned
Securities owned, at fair value	387,652	551,286
Derivative contracts:
Total	412,589	580,369
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	36,384	60,977
Derivative contracts:
Derivative contracts	44	287
Total	36,428	61,264
Level 1 | Money markets
Securities owned
Securities owned, at fair value	0	31
Level 1 | Futures
Derivative contracts:
Derivative contracts	44	287
Level 1 | U.S. Treasury securities
Securities owned
Securities owned, at fair value	362,815	505,875
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	25,006	42,298
Level 1 | Corporate equities | Corporate equities
Securities owned
Securities owned, at fair value	24,837	45,380
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	11,378	18,679
Level 2
ASSETS
Deposits with clearing organizations	0
Securities owned
Securities owned, at fair value	79,166	51,414
Investments	7,068	12,970
Derivative contracts:
Total	87,996	64,476
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	16,384	10,981
Derivative contracts:
Derivative contracts	1,761	81
Total	18,145	11,062
Level 2 | Auction rate securities
Securities owned
Securities owned, at fair value		0
Level 2 | TBAs
Derivative contracts:
Derivative contracts, total	1,762	92
Derivative contracts:
Derivative contracts	1,761	81
Level 2 | U.S. Agency securities
Securities owned
Securities owned, at fair value	6,012	5,622
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	3	4
Level 2 | Sovereign obligations
Securities owned
Securities owned, at fair value	9,502	1,494
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	9,048
Level 2 | Corporate debt and other obligations
Securities owned
Securities owned, at fair value	9,844	8,111
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	2,905	2,515
Level 2 | Mortgage and other asset-backed securities
Securities owned
Securities owned, at fair value	1,882	3,889
Level 2 | Municipal obligations
Securities owned
Securities owned, at fair value	30,126	18,520
Level 2 | Convertible bonds
Securities owned
Securities owned, at fair value	21,800	13,778
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	4,428	8,462
Level 3
ASSETS
Deposits with clearing organizations	0
Securities owned
Securities owned, at fair value	31,776	31,804
Derivative contracts:
Total	31,776	31,804
Derivative contracts:
Derivative contracts	0	0
Total	0	0
Level 3 | Auction rate securities
Securities owned
Securities owned, at fair value	$ 31,776	$ 31,804

[1] (1) Certain prior period reported amounts were reclassified to conform to the current period presentation, See Note 2.