The conversion option in life insurance

Multi-state models for evaluating conversion options in life insurance

“…To this end we first derive transition probabilities for the model and then we develop the evaluation procedure by analyzing the TIP and PIP contracts and the conversion option. The obtained results represent the generalization of the results of [17] in a more general framework. Particularly, we show that the value of the conversion option depends on many parameters that are contemporary managed by our model such as the health status evolution of the policyholder, the age of the policyholder and the chronological time effect due to medical-scientific progress.…”

“…Now we are in the position of computing the value of the conversion option by substituting Eqs (23) and (24) in Formula (17). Some algebra gives the following representation:…”

“…In analogy with the financial options, we can define a set where it is convenient to exercise the conversion option. This is a prerogative of the adopted multi-state model because in the paper [17], if the insured person was still alive at the conversion time it was always convenient to prolong the coverage by exercising the option. However, in our more general framework, this is not the case, because given the initial 0-scenario (i, u, x) it is possible after n years that the insured person improves considerably the health state and the prospective expectation of a prolonged life.…”

“…The literature on conversion option is not large and the main reference is represented by the article [17] where a valuation model was constructed based on mortality tables and then extended to a Lee-Carter model of mortality. A related article is [15] where the author considered an exchange option that is available in Norway.…”