Projections using replicating portfolios for insurance liabilities

For insurers it is important to value and price their assets and liabilities in a market consistent manner. In this thesis the replicating portfolio technique will be applied for the fair valuation of three different insurance products: pure cash flow, inflation linked, and option embedded. To construct the replicating portfolios we make use of the ordinary least squares and constrained least square approach. The main concern is the maximum (relative) error of the replicating portfolio. We find that this maximum is highly dependent on the product which is evaluated, but even the worst case remains limited to deviation of at most 3,5% of the products true value. In the next step the replicating portfolios are used to make projections of the products. It is found that the errors of the projections are equal to the initial error with accumulated interest. We then argue that the distribution of these projection errors is equal to the errors of the fit of the replicating portfolio. Hence, we conclude that the fit of the replicating portfolio is of vital importance to the quality of the projections.