Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option

Mustapha Abdul-Rahaman

doi:10.11648/j.ajmcm.20180301.12

Abstract

Life insurance contracts are priced and analysed using techniques from actuarial and modern financial mathematics, which requires that, the conditions for the risk-neutral valuation are fulfilled and that, a specified underlying security and an equivalent martingale measure must exist. This paper analysed life insurance endowment policy, paid by sequence of periodical premiums in Ghana with a guaranteed minimum return to the policyholder. Again, this paper presents two premium determination schemes for the insurance policy, the constant premium case and the periodical adjustment case in which both the benefit and the periodical premiums are annually adjusted in relation to the performance of a reference portfolio. It was realized that, with rising guaranteed interest rate, the rate of return on the reference portfolio, the premiums of the whole contract decreased both in the constant and the periodical adjustment cases whiles an increase in the participating coefficient and age of the insured led to an increase in the whole premium both in the constant and periodical adjustment cases. Also, it was revealed that, the premium of the non-surrendered bonus option is smaller in the constant premium case than in the periodical adjustment case and the premium of the bonus option in the surrendered participating policy looks cheap in the constant premium case than in the periodical adjustment case. Thus, it’s about 1.03% and 6.95% respectively of the total premium for the constant and for the periodical adjustment cases.

Highlights

Insurance provides a medium through which contingent future losses are exchange for fixed premium payments [18]
The equivalent principle is the consequent of this rationale as a basis for pricing insurance products such that the present value of premiums equals the present value of the expected future losses
It was revealed that; the premium of the non-surrendered bonus option is smaller in the constant premium case than in the periodical adjustment case and the premium of the bonus option in the surrendered participating policy looks cheap in the constant premium case than in the periodical adjustment case

Summary

Introduction

Insurance provides a medium through which contingent future losses are exchange for fixed premium payments [18]. The equivalent principle is the consequent of this rationale as a basis for pricing insurance products such that the present value of premiums equals the present value of the expected future losses. Pricing both life and non-life insurance products originates from the equivalent principle, its application as observed by Biener requires divergent approaches in relation to different properties of risk in different line of business [6]. People might become ill and lose their income to pay off medical bills Individuals or their relatives may die of illness or accidents. Bacinello defined participating policy as a contract in which the policyholder is entitled to a share of the excess profit if the realized interest rate during the insurance period is above the assumed interest rate [1]

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