Dependent interest and transition rates in life insurance

Kristian Buchardt

doi:10.1016/j.insmatheco.2014.01.004

Dependent interest and transition rates in life insurance

Kristian Buchardt

Institut for Matematiske Fag

8 Citationer (Scopus)

Abstract

For market consistent life insurance liabilities modelled with a multi-state Markov chain, it is of importance to consider the interest and transition rates as stochastic processes, for example in order to consider hedging possibilities of the risks, and for risk measurement. In the literature, this is usually done with an assumption of independence between the interest and transition rates. In this paper, it is shown how to valuate life insurance liabilities using affine processes for modelling dependent interest and transition rates. This approach leads to the introduction of so-called dependent forward rates. We propose a specific model for surrender modelling, and within this model the dependent forward rates are calculated, and the market value and the Solvency II capital requirement are examined for a simple savings contract.

Originalsprog	Engelsk
Tidsskrift	Insurance: Mathematics and Economics
Vol/bind	55
Sider (fra-til)	167–179
ISSN	0167-6687
DOI	https://doi.org/10.1016/j.insmatheco.2014.01.004
Status	Udgivet - mar. 2014

Adgang til dokumentet

10.1016/j.insmatheco.2014.01.004

Citationsformater

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AB - For market consistent life insurance liabilities modelled with a multi-state Markov chain, it is of importance to consider the interest and transition rates as stochastic processes, for example in order to consider hedging possibilities of the risks, and for risk measurement. In the literature, this is usually done with an assumption of independence between the interest and transition rates. In this paper, it is shown how to valuate life insurance liabilities using affine processes for modelling dependent interest and transition rates. This approach leads to the introduction of so-called dependent forward rates. We propose a specific model for surrender modelling, and within this model the dependent forward rates are calculated, and the market value and the Solvency II capital requirement are examined for a simple savings contract.

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