Financial Instruments and Other Inventory Positions Owned and Financial Instruments and Other Inventory Positions Sold, but Not Yet Purchased - Schedule of Financial Instruments Owned and Financial Instruments Sold, but Not Yet Purchased by Type (Details) - USD ($) $ in Thousands	Sep. 30, 2021	Dec. 31, 2020
Financial instruments and other inventory positions owned:
Equity securities	$ 5,780	$ 1,349
Convertible securities	150,979	146,088
Fixed income securities	21,556	18,432
Taxable securities	23,330	6,267
Tax-exempt securities	117,212	67,944
Short-term securities	56,486	28,592
Mortgage-backed securities	13	13
U.S. government agency securities	51,838	9,146
U.S. government securities	48	100,275
Derivative contracts	23,573	23,446
Total financial instruments and other inventory positions owned	450,815	401,552
Financial instruments and other inventory positions sold, but not yet purchased:
Equity securities	62,407	105,190
Fixed income securities	5,468	18,789
U.S. government securities	58,277	21,669
Derivative contracts	5,397	5,382
Total financial instruments and other inventory positions sold, but not yet purchased	131,549	151,030
Financial instruments and other inventory positions owned and pledged as collateral	$ 117,615	$ 130,703