A recursive approach to mortality-linked derivative pricing

作者：Shang Zhaoning^*; Goovaerts Marc; Dhaene Jan

来源：Insurance: Mathematics and Economics , 2011, 49(2): 240-248.

DOI：10.1016/j.insmatheco.2011.03.003

• Mortality-linked derivative
• Diffusion process
• Transition density function
• Feynman-Kac integral

In this paper, we develop a recursive method to derive an exact numerical and nearly analytical representation of the Laplace transform of the transition density function with respect to the time variable for time-homogeneous diffusion processes. We further apply this recursion algorithm to the pricing of mortality-linked derivatives. Given an arbitrary stochastic future lifetime 7, the probability distribution function of the present value of a cash flow depending on 7 can be approximated by a mixture of exponentials, based on Jacobi polynomial expansions. In case of mortality-linked derivative pricing, the required Laplace inversion can be avoided by introducing this mixture of exponentials as an approximation of the distribution of the survival time T in the recursion scheme. This approximation significantly improves the efficiency of the algorithm.

• 出版日期2011-9