TY - JOUR

T1 - Longevity bond pricing under stochastic interest rate and mortality with regime-switching

AU - Shen, Yang

AU - Siu, Tak Kuen

PY - 2013/1

Y1 - 2013/1

N2 - We develop a flexible model to value longevity bonds which incorporates several important sources of risk, namely, interest rate risk, mortality risk and the risk due to structural changes in economic and environmental conditions. In particular, Markov, regime-switching, jump-diffusion models are used to describe stochastic movements of short-term interest rate and force of mortality. These models capture jumps in short rate and mortality rate and the impacts of economic and environmental fundamentals on their movements over time. Using the concept of stochastic flows, we derive an exponential affine form of the longevity bond price in the proposed joint stochastic interest rate and mortality models. In particular, a representation for the exponential affine form of the longevity bond price is obtained in terms of fundamental matrix solutions of linear, matrix-valued, ordinary differential equations.

AB - We develop a flexible model to value longevity bonds which incorporates several important sources of risk, namely, interest rate risk, mortality risk and the risk due to structural changes in economic and environmental conditions. In particular, Markov, regime-switching, jump-diffusion models are used to describe stochastic movements of short-term interest rate and force of mortality. These models capture jumps in short rate and mortality rate and the impacts of economic and environmental fundamentals on their movements over time. Using the concept of stochastic flows, we derive an exponential affine form of the longevity bond price in the proposed joint stochastic interest rate and mortality models. In particular, a representation for the exponential affine form of the longevity bond price is obtained in terms of fundamental matrix solutions of linear, matrix-valued, ordinary differential equations.

UR - http://www.scopus.com/inward/record.url?scp=84871659940&partnerID=8YFLogxK

U2 - 10.1016/j.insmatheco.2012.11.006

DO - 10.1016/j.insmatheco.2012.11.006

M3 - Article

VL - 52

SP - 114

EP - 123

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 1873-5959

IS - 1

ER -