Transferência do risco de longevidade: modelagem e precificação sob o Regime Solvência II

Abstract

With the evolution of life expectancy, pension funds and insurance companies that have benefit plans defined have faced one of the greatest and least understood adversities: the risk of longevity, which is the possibility of unexpected improvements in the lifetime of the participants of the plan. This is represented by the increase in the average period of payment of benefits, impacting on changes in actuarial liabilities. One possible mitigation route is its transfer through an operation called securitization. Through a hedge, it is possible for the entity to transfer the risk of longevity to the capital market using derivatives. This transaction is based on a financial agreement that establishes the exchange of payments among the involved counterparts considering the mortality or survival rate of a said population. This operation is called longevity-linked security. In this work, the efforts are focused on s-forward as an object of study. This derivative consists of a contract established between two counterparties, which stipulate the exchange of payments based on the survival rate. The entity that wishes to transfer the risk of longevity makes fixed payments throughout the life of the contract, while the counterparty makes floating payments based on the difference between the expected and the realized survival. One of the challenges for the development of the market for longevity risk transfer is the pricing of these instruments. The price that the entity will have to pay to carry out the transfer is calling the risk premium. As a general objective of this work, the determination of the maximum value of the premium that an entity is willing to pay to transfer the risk of longevity is proposed. It is based on an s-forward and taking into account the regulations established by Solvency II. To do so, it was necessary to perform mortality modeling using the Lee-Carter, Cairns-Blake-Dowd (CBD), APC, Renshaw and Haberman (RH), M7 and Plat models. Among these, the Lee-Carter model presented the best fit and was used to design mortality using an ARIMA (0,1,0). The results show that the values increase according to the evolution of the maturity time of contracts and cohorts.