Fair value measurements - Schedule of Assets and Liabilities Measured at Fair Value on Recurring Basis (Details) - USD ($) $ in Thousands	Sep. 30, 2025	Dec. 31, 2024
Assets
Deposits with clearing organizations	$ 27,993	$ 28,071
Securities owned:
Securities owned, at fair value	1,316,093	1,108,206
Investments	17,146	17,983
Trade claim		2,684
Loans	734	432
Total	1,362,049	1,157,376
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	258,856	98,892
Derivative contracts: (2)
Derivative contracts, total	1,068	1,071
Total	259,924	99,963
Derivative contracts, total	83
U.S. Treasury securities
Securities owned:
Securities owned, at fair value	1,216,287	995,420
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	230,586	82,767
U.S. Agency securities
Securities owned:
Securities owned, at fair value	6,205	3,691
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	27	4
Sovereign obligations
Securities owned:
Securities owned, at fair value	6,403
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	4,599
Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	10,529	9,423
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	1,143	11
Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	2,095	8,954
Municipal obligations
Securities owned:
Securities owned, at fair value	17,259	34,704
Convertible bonds
Securities owned:
Securities owned, at fair value	17,222	21,938
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	13,521	4,998
Corporate equities
Securities owned:
Securities owned, at fair value	32,937	23,873
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	8,980	11,112
Money markets
Securities owned:
Securities owned, at fair value	7,028	7,551
Auction rate securities
Securities owned:
Securities owned, at fair value	128	2,652
Futures
Derivative contracts: (2)
Derivative contracts, total	982	1,071
TBAs
Derivative contracts: (2)
Derivative contracts, total	86
Derivative contracts, total	83
Level 1
Assets
Deposits with clearing organizations	27,993	28,071
Securities owned:
Securities owned, at fair value	1,254,554	1,026,844
Investments	0	978
Trade claim		0
Loans	0	0
Total	1,282,547	1,055,893
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	239,566	93,879
Derivative contracts: (2)
Derivative contracts, total	982	1,071
Total	240,548	94,950
Derivative contracts, total	0
Level 1 | U.S. Treasury securities
Securities owned:
Securities owned, at fair value	1,216,287	995,420
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	230,586	82,767
Level 1 | U.S. Agency securities
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 1 | Sovereign obligations
Securities owned:
Securities owned, at fair value	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0
Level 1 | Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 1 | Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	0	0
Level 1 | Municipal obligations
Securities owned:
Securities owned, at fair value	0	0
Level 1 | Convertible bonds
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 1 | Corporate equities
Securities owned:
Securities owned, at fair value	31,767	23,873
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	8,980	11,112
Level 1 | Money markets
Securities owned:
Securities owned, at fair value	6,500	7,551
Level 1 | Auction rate securities
Securities owned:
Securities owned, at fair value	0	0
Level 1 | Futures
Derivative contracts: (2)
Derivative contracts, total	982	1,071
Level 1 | TBAs
Derivative contracts: (2)
Derivative contracts, total	0
Derivative contracts, total	0
Level 2
Assets
Deposits with clearing organizations	0	0
Securities owned:
Securities owned, at fair value	58,268	78,710
Investments	17,146	17,005
Trade claim		0
Loans	734	432
Total	76,231	96,147
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	19,290	5,013
Derivative contracts: (2)
Derivative contracts, total	86	0
Total	19,376	5,013
Derivative contracts, total	83
Level 2 | U.S. Treasury securities
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 2 | U.S. Agency securities
Securities owned:
Securities owned, at fair value	6,205	3,691
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	27	4
Level 2 | Sovereign obligations
Securities owned:
Securities owned, at fair value	6,403
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	4,599
Level 2 | Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	8,556	9,423
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	1,143	11
Level 2 | Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	2,095	8,954
Level 2 | Municipal obligations
Securities owned:
Securities owned, at fair value	17,259	34,704
Level 2 | Convertible bonds
Securities owned:
Securities owned, at fair value	17,222	21,938
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	13,521	4,998
Level 2 | Corporate equities
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 2 | Money markets
Securities owned:
Securities owned, at fair value	528	0
Level 2 | Auction rate securities
Securities owned:
Securities owned, at fair value	0	0
Level 2 | Futures
Derivative contracts: (2)
Derivative contracts, total	0	0
Level 2 | TBAs
Derivative contracts: (2)
Derivative contracts, total	86
Derivative contracts, total	83
Level 3
Assets
Deposits with clearing organizations	0	0
Securities owned:
Securities owned, at fair value	3,271	2,652
Investments	0	0
Trade claim		2,684
Loans	0	0
Total	3,271	5,336
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Derivative contracts: (2)
Derivative contracts, total	0	0
Total	0	0
Derivative contracts, total	0
Level 3 | U.S. Treasury securities
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 3 | U.S. Agency securities
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 3 | Sovereign obligations
Securities owned:
Securities owned, at fair value	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0
Level 3 | Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	1,973	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 3 | Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	0	0
Level 3 | Municipal obligations
Securities owned:
Securities owned, at fair value	0	0
Level 3 | Convertible bonds
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 3 | Corporate equities
Securities owned:
Securities owned, at fair value	1,170	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 3 | Money markets
Securities owned:
Securities owned, at fair value	0	0
Level 3 | Auction rate securities
Securities owned:
Securities owned, at fair value	128	2,652
Level 3 | Futures
Derivative contracts: (2)
Derivative contracts, total	0	$ 0
Level 3 | TBAs
Derivative contracts: (2)
Derivative contracts, total	0
Derivative contracts, total	$ 0