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A recursive approach to mortality-linked derivative pricing

Authors
Journal
Insurance Mathematics and Economics
0167-6687
Publisher
Elsevier
Publication Date
Volume
49
Issue
2
Identifiers
DOI: 10.1016/j.insmatheco.2011.03.003
Keywords
  • Mortality-Linked Derivative
  • Diffusion Process
  • Transition Density Function
  • Feynman–Kac Integral
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract 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 T , the probability distribution function of the present value of a cash flow depending on T 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.

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