Valuation of contingent claims with stochastic interest rate and mortality driven by Lévy processes

Abstract

In this paper, we consider a model with stochastic interest rate and stochastic mortality, which is driven by a Lévy process. Under the assumption that the stochastic mortality and interest rate are dependent, we discuss the valuation of life insurance contracts. Employing the method of change of measure together with the Bayes’ rule, we present the pricing formulas in closed form for the survival and death benefit models. Finally, numerical experiments illustrate the effects of some parameters.

Keywords:

• Stochastic mortality
• stochastic interest rate
• Lévy process

Funding

This work was supported by the 111 Project (B14019), National Natural Science Foundation of China (11701372, 11601320, 11501211, 11571113), Natural Science Foundation of Shanghai (16ZR1422400). ``Xunlun'' Program of Shanghai Lixin University of Accounting and Finance.

Notes

1 For $B_S(0,T,1),$ though the absolute values of the differences are small, the prices of survival benefit for T = 35, 40 with jump are about a half of those without jump.