Actuarial and Financial Valuation of Catastrophe Bonds
Among different types of insurance-linked security instruments existing in capital markets, catastrophe bonds are important for insurance companies. Such a contract includes both financial and actuarial risks, making their valuation procedure quite complicated from a theoretical perspective. The financial valuation of catastrophe bonds is based on the idea of arbitrage-free pricing and a risk-neutral measure approach. In this paper, we provide a valuation based on the actuarial methodology in which the best estimate of discounted loss plus a risk margin are computed under the physical measure. To do so, we introduce the variance premium principle and achieve a closed-form formula for the catastrophe bond price. As it is impossible to determine the physical probability distribution associated with the aggregate losses explicitly, we apply the Monte-Carlo simulation technique.