High correlations between risks can increase required insurer capital and/orreduce the availability of insurance. For such insurance lines, securitizationis rapidly emerging as an alternative form of risk transfer. The ultimatesuccess of securitization in replacing or complementing traditional insuranceand reinsurance products depends on the ability of securitization to facilitateand/or be facilitated by insurance contracts. We consider how insuredlosses might be decomposed into separate components, one of which is atype of systemic risk that is highly correlated amongst insureds. Such acorrelated component might conceivably be hedged directly by individuals,but is more likely to be hedged by the insurer. We examine how insurancecontracts may be designed to allow the insured a mechanism to retain all orpart of the systemic component. Examples are provided, which illustrate ourmethodology in several types of insurance markets subject to systemic risk.