The pricing of hedging longevity risk with the help of annuity securitizations: An application to the German market

摘要

Purpose - The purpose of this paper is to develop a model to hedge annuity portfolios against increases in life expectancy. Across the globe, and in the industrial nations in particular, people have seen an unprecedented increase in their life expectancy over the past decades. The benefits of this apply to the individual, but the dangers apply to annuity providers. Insurance companies often possess no effective tools to address the longevity risk inherent in their annuity portfolio. Securitization can serve as a substitute for classic reinsurance, as it also transfers risk to third parties. Design/methodology/approach - This paper extends on methods insurer's can use to hedge their annuity portfolio against longevity risk with the help of annuity securitization. Future mortality rates with the Lee-Carter-model and use the Wang-transformation to incorporate insurance risk are forecasted. Based on the percentile trenching method, where individual tranches are aligned to Standard & Poor's ratings, we price an inverse survivor bond. This bond offers fix coupon payments to investors, while the principal payments are at risk and depend on the survival rate within the underlying portfolio. Findings - The contribution to the academic literature is threefold. On the theoretical side, building on the work of Kim and Choi (2011), we adapt their pricing model to the current market situation. Putting the principal at risk instead of the coupon payments, the insurer is supplied with sufficient capital to cover additional costs due to longevity. On the empirical side, the method for the German market is specified. Inserting specific country data into the model, price sensitivities of the presented securitization model are analyzed. Finally, in a case study, the procedure to the annuity portfolio of a large German life insurer is applied and the price of hedging longevity risk is calculated. Practical implications - To illustrate the implication of this bond structure, several sensitivity tests were conducted before applying the pricing model to the retail sample annuity portfolio from a leading German life insurer. The securitization structure was applied to calculate the securitization prices for a sample portfolio from a large life insurance company. Social implications - The findings contribute to the current discussion about how insurers can face longevity risk within their annuity portfolios. The fact that the rating structure has such a severe impact on the overall hedging costs for the insurer implies that companies that are willing to undergo an annuity securitization should consider their deal structure very carefully. In addition, we have pointed out that in imperfect markets, the retention of the equity tranche by the originator might be advantageous. Nevertheless, one has to bear in mind that by this behavior, the insurer is able to reduce the overall default risk in his balance sheet by securitizing a life insurance portfolio; however, the fraction of first loss pieces from defaults increases more than proportionally. The insurer has to take care to not be left with large, unwanted remaining risk positions in his books. Originality/value - In this paper, we extend on methods insurer's can use to hedge their annuity portfolio against longevity risk with the help of annuity securitization. To do so, we take the perspective of the issuing insurance company and calculate the costs of hedging in a four-step process. On the theoretical side, building on the work of Kim and Choi (2011), we adapt their pricing model to the current market situation. On the empirical side, we specify the method for the German market. Inserting specific country data into the model, price sensitivities of the presented securitization model are analyzed.