Hedging Embedded Options in Life Insurance Products

Life insurance products often contain embedded options in the form of profit sharing and guaranteed returns on premiums deposited by the customer. The value of these embedded options is exposed to market risks. This thesis describes a method to find good hedge portfolios of swaptions to hedge the market risks of the embedded options. In addition, a method is described to monitor and clarify the hedge effectiveness based on the underlying risk drivers. To find a good hedge portfolio of swaptions, an objective function is defined first. The objective value is based on four performance measures for the quality of a hedge portfolio. The performance measures quantify the mismatch between the swaptions and the embedded options in their sensitivity to different market risks. Two evolutionary algorithms (EAs) are used to compose hedge portfolios of swaptions that minimize the objective function. One EA searches for an optimal subset of swaptions within a given set of swaptions. This EA is used to unwind swaptions that are not effective anymore. The other EA searches for good swaptions to be added that will improve the portfolio. The results show that the algorithm generally produces good solutions with respect to the objective function and the four performance measures. The hedge effectiveness is measured with the Dollar Offset method. The Dollar Offset method expresses the hedge effectiveness as the ratio of the change in value of the hedging instrument and the change in value of the hedged item. To clarify deviations from the desired effectiveness, we use a method to reconcile the changes of the swaptions and the embedded options, based on their underlying risk drivers. This gives insight in the causes of possible mismatches between the change in value of the swaptions and the change in value of the embedded options.