Fair value measurements - Assets and Liabilities Measured at Fair Value on Recurring Basis (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021
ASSETS
Deposits with clearing organizations	$ 41,389	$ 29,083
Securities owned:
Securities owned, at fair value	662,677	634,504	[1]
Securities owned and sold, fair value	662,677	634,504
Investments	8,650	12,970
Derivative contracts
Total	712,716	676,649
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	94,893	71,958	[1]
Derivative contracts:
Derivative contracts	149	368
Total	95,042	72,326
Corporate equities
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	11,315	18,679
Money markets
Securities owned:
Securities owned, at fair value	78	31
Auction rate securities
Securities owned:
Securities owned, at fair value	33,123	31,804
TBAs
Derivative contracts
Derivative contracts, total		92
Derivative contracts:
Derivative contracts		81
Futures
Derivative contracts:
Derivative contracts	149	287
U.S. Treasury securities
Securities owned:
Securities owned, at fair value	519,569	505,875
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	72,842	42,298
U.S. Agency securities
Securities owned:
Securities owned, at fair value	19,063	5,622
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	6	4
Sovereign obligations
Securities owned:
Securities owned, at fair value	345	1,494
Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	12,174	8,111
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	6,931	2,515
Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	2,050	3,889
Municipal obligations
Securities owned:
Securities owned, at fair value	31,838	18,520
Convertible bonds
Securities owned:
Securities owned, at fair value	17,139	13,778
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	3,799	8,462
Corporate equities | Corporate equities
Securities owned:
Securities owned, at fair value	27,298	45,380
Level 1
ASSETS
Deposits with clearing organizations	41,389	29,083
Securities owned:
Securities owned, at fair value	546,945	551,286
Derivative contracts
Total	588,334	580,369
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	84,157	60,977
Derivative contracts:
Derivative contracts	149	287
Total	84,306	61,264
Level 1 | Money markets
Securities owned:
Securities owned, at fair value	78	31
Level 1 | Futures
Derivative contracts:
Derivative contracts	149	287
Level 1 | U.S. Treasury securities
Securities owned:
Securities owned, at fair value	519,569	505,875
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	72,842	42,298
Level 1 | Corporate equities
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	11,315	18,679
Level 1 | Corporate equities | Corporate equities
Securities owned:
Securities owned, at fair value	27,298	45,380
Level 2
Securities owned:
Securities owned, at fair value	82,609	51,414
Investments	8,650	12,970
Derivative contracts
Total	91,259	64,476
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	10,736	10,981
Derivative contracts:
Derivative contracts	0	81
Total	10,736	11,062
Level 2 | TBAs
Derivative contracts
Derivative contracts, total		92
Derivative contracts:
Derivative contracts		81
Level 2 | U.S. Agency securities
Securities owned:
Securities owned, at fair value	19,063	5,622
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	6	4
Level 2 | Sovereign obligations
Securities owned:
Securities owned, at fair value	345	1,494
Level 2 | Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	12,174	8,111
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	6,931	2,515
Level 2 | Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	2,050	3,889
Level 2 | Municipal obligations
Securities owned:
Securities owned, at fair value	31,838	18,520
Level 2 | Convertible bonds
Securities owned:
Securities owned, at fair value	17,139	13,778
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	3,799	8,462
Level 3
Securities owned:
Securities owned, at fair value	33,123	31,804
Derivative contracts
Total	33,123	31,804
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	0
Derivative contracts:
Derivative contracts	0	0
Total	0	0
Level 3 | Auction rate securities
Securities owned:
Securities owned, at fair value	$ 33,123	$ 31,804

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