Where frequency and severity of risks, e.g. of catastrophic risks are unknown, as is the case, e.g., for environmental risks, health risks, nuclear reactor risks, and satellite risks, ordinary insurance contracts on occasion are likely to result in claims which an insurer cannot cover. For efficient allocation of risk bearing, an insurance contract is combined or "bundled" with a derivative security. Insurance is contingent on the frequency of the insured event as observed, and the derivative security has a payoff which depends on that frequency. Thus, the derivative security is a contract which is contingent on an index established as a standardized measure of a risk, e.g. of environmental conditions such as El Niño versus La Niña, and/or temperature measures such as heating degree days (HDD), cooling degree days (CDD) and/or precipitation measures in a specific geographic region and during a specified time period.