Natural Hedging Using Multi-population Mortality Models
No mortality projection model can capture future mortality changes accurately so that the actual mortality rates are different from the projected ones. The movement of mortality rates has oppositive impacts on the values of life insurance and annuity products, which creates a chance of nature hedge for both life insurer and annuity provider. A life insurer and an annuity provider can swap their life insurance and annuity business each other to form their own portfolios for natural hedge. This project is mainly focused on determining the weights of a portfolio of life insurance and annuity products by minimizing the variance of the loss function of the portfolio to reduce mortality and longevity risks for each of the life insurer and the annuity provider. Four Lee-Carter-based models are applied to model the co-movement of two populations of life insurance and annuity insureds, and then determine the weights for comparisons. The block bootstrap model, a model-/parameter-free approach, is also adopted with numerical illustrations to compare the hedging performances among the four models.