The quota market is the instrument through which fishing operations under an individual transferable quota (ITQ) system achieve greater efficiency. It allows fishing companies to optimally configure their quota portfolios to their catches. Globally, fisheries corresponding to ~25% of landings have adopted ITQ systems. However, there is surprisingly little empirical information on quota markets functioning. Here we study the development of quota share and lease markets and assess market activity and functioning for the cod fishery in Iceland. We use a social network analysis to assess changes in four Icelandic quota markets, distinguished by boat size (large versus small) and permanence of transfers (leases versus shares). The quota market for permanent trades in small-boat quota shows a sharp increase in trade and network connectivity between 2004 and 2006, resulting in a high rate of quota concentration. The quota markets for permanent quota shares were the most fragmented and sparse during the years of the financial crash in Iceland and never regain the same activity. Our results suggest that quota systems evolve towards a consolidated state and that their markets are not entirely resilient to financial instability. We also found some evidence that better-connected traders could sell quota at higher prices in the lease markets, though price dispersion was generally low.