Abstract
In this paper we propose a multi-state model for the evaluation of the conversion option contract. The multi-state model is based on age-indexed semi-Markov chains that are able to reproduce many important aspects that influence the valuation of the option such as the duration problem, the time non-homogeneity and the ageing effect. The value of the conversion option is evaluated after the formal description of this contract.
Highlights
IntroductionA general approach based on semi-Markov processes has been applied to problems of disability insurance in recent years, see [16, 4, 5, 14]
The conditional present value of premiums given the possibility to convert is equal to the conditional present value of premiums from the temporary insurance policy (TIP) contract plus the conditional present value of premiums from the permanent insurance policy (PIP) calculated under the n-scenario (aZ(n), B(n), A(n)) and discounted at time zero if this scenario does not belong to the exercise set plus the expected payment to face by converting the option if the n-scenario belongs to the exercise set
The valuation of conversion options in life insurance is an important subject in modern actuarial mathematics
Summary
A general approach based on semi-Markov processes has been applied to problems of disability insurance in recent years, see [16, 4, 5, 14] Their appropriateness is due to the rejection of the geometric (exponential in continuous time model) distribution hypothesis for modeling the waiting times in a health status before making a transition in another state. In this paper we focus on the evaluation of the conversion options when an ageindexed semi-Markov multi-state model describes the evolution of the health status of the policyholder To this end we first derive transition probabilities for the model and we develop the evaluation procedure by analyzing the TIP and PIP contracts and the conversion option. The paper ends with some conclusions and suggestions for further research
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