We conduct a head-to-head comparison of central and bilateral clearing to evaluate the impact of market structure on market stability. We introduce the concept of “all-or-nothing” payouts, whereby counterparties are assumed to either discharge their obligations in full or not at all. We argue that this assumption appropriately reflects payout incentives in centrally cleared markets and, in times of market stress, could characterize bilateral markets as well. If this all-or-nothing assumption is made for both structures, we find that central clearing enhances network stability in the event of a severe shock. Our results are ambiguous for small shocks. In addition, we find that the stability benefits of central clearing are higher for networks with large potential gains from multilateral netting. In contrast, when we replace the all-or-nothing assumption with the pro-rata payout assumption generally made in the literature, we find that the bilateral structure is more stable than the centrally cleared structure. Thus, our assessment of the relative benefits of central clearing depends on whether or not defaulters in the bilateral market are likely to make partial payments under stressed conditions.