Pricing the property claim service (PCS) catastrophe insurance options using gamma distribution

The catastrophic events like earthquakes, hurricanes or flooding are characteristics for some areas, a properly calculated annual premium would be closely as high as the loss insured. From an actuarial perspective, such events constitute the risk that are not insurable. On the other hand people living in such areas need protection. In order to securitize the catastrophe risk, futures or options based on a loss index could be considered. Chicago Board of Trade launched a new class of catastrophe insurance options based on new indices provided by Property Claim Services (PCS). The PCS-option is based on the Property Claim Service Index (PCS-Index). The index are used to determine and payout in writing index-based insurance derivatives. The objective of this paper is to price PCS Catastrophe Insurance Option based on PCS Catastrophe index. Gamma Distribution is used to estimate PCS Catastrophe index distribution.