Since the 2007 Financial Crisis, regulators have been very interested in modeling and measuring systemic risk in the financial system. In this study, a network approach is taken to characterize the systemic risk of two nontraditional insurance industries: the bond insurer industry and the CDS market. These industries were chosen since traditional insurance industries do not generate significant systemic risk. The network model for bond insurers demonstrates that after an exogenous shock (a fall in the housing market), bond insurers become insolvent not because of the cross holding of assets but because of the drastic increase in their liabilities. A second, structurally different network model of the CDS market shows how certain parameters of a network can affect the expected loss of the system relative to the initial loss caused by a default. This model also demonstrates how a clearinghouse stymies loss propagation and highlights the usefulness of important data such as counterparty exposures that are not publicly available. If regulators collected counterparty exposure data, they could use it in this kind of model to identify systemically important institutions and better monitor the financial system.