Pricing Longevity Bonds Under the Uncertainty Theory Framework

Abstract

This paper aims to develop a new pricing approach for longevity bonds under the uncertainty theory framework. First, we describe the life expectancy by a canonical uncertain process and illustrate the dynamic of short interest rate via an uncertain Vasicek interest rate model. Then, based on these descriptions, we construct an uncertain survival index model and present its procedure for parameter estimation. By applying the chain rule, we derive a pricing formula of the uncertain zero-coupon bond. Considering that the financial market is incomplete, we put forward an uncertain distortion operator. Furthermore, based on the uncertain survival index, the uncertain zero-coupon bond pricing formula and the uncertain distortion operator, we develop a pricing formula of the uncertain longevity bond and its calculation algorithm. Finally, a numerical example is shown to illustrate the influence of parameters on the price of the uncertain longevity bond.