Modelling and Valuation of Guarantees in With-Profit and Unitised With Profit Life Insurance Contracts

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Abstract
The purpose of this paper is to develop suitable valuation techniques for the broad category of participating life insurance policies. The nature of the liability implied by these contracts allows treating them as options written on the reference portfolio backing the policy. Consequently, our valuation approach is based on the classical contingent claim theory; in particular, Monte Carlo techniques are used to compute the values of the so called 'policy reserve', that is the guaranteed payoff and the reversionary bonus, and the terminal bonus. The numerical results obtained are used to investigate the sensitivity of the policy reserve and the terminal bonus to changes in the model parameters. The paper also addresses the issue of a fair contract design for with-profit life insurance policies. Bearing in mind that the parameters characterizing the financial market are in general not under the control of the life insurance offce, the implemented valuation procedure is used to determine the feasible set of design parameters that would lead to a fair contract.