Fair valuations of insurance policies under multiple risk factors: A flexible lattice approach

Pierre Devolder (), Emilio Russo and Alessandro Staino
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Pierre Devolder: Université catholique de Louvain, LIDAM/ISBA, Belgium
Emilio Russo: University of Calabria
Alessandro Staino: University of Calabria

No 2024010, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: We propose a flexible lattice model to evaluate the fair value of insurance contracts embedding both financial and actuarial risk factors. Flexibility relies on the ability of the model to manage different specifications of the correlated processes governing interest rate, mortality, and fund dynamics, thus allowing the insurer to make the most appropriate choices. The model is also able to handle additional guarantees like a surrender opportunity for which explicit formulae are not available being it similar to an American derivative. The model discretizes mortality and interest rate dynamics through two different binomial lattices and then combines them into a bivariate tree characterized by the presence of four branches for each node. The probability of each branch is defined to replicate the correlation affecting the two processes. The bivariate model is useful to compute the value of survival zero coupon bond. When adding another source of risk, such as the fund dynamics for evaluating fund-linked insurance products, we model it through a bivariate tree that captures the influence of the interest rate on its drift term. Then, the mortality risk is embedded by defining a trivariate tree presenting eight branches emanating from each node with probabilities defined in order to capture the correlations of the processes. Extensive numerical experiments assess the model accuracy by considering some stylized policies, but the model application is not limited to them being it able to manage different contract specifications.

Keywords: Stochastic interest rate; stochastic mortality; binomial algorithms; multiple risk factors; lattice models (search for similar items in EconPapers)
Pages: 25
Date: 2024-02-12
Note: In: ASTIN Bulletin, 2024
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2024010

DOI: 10.1017/asb.2024.5

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