Mortality modelling with renewal process and optimal hedging strategy under basis risk

In this thesis, we address the risks that are related to the random residual lifetime of insureds. These risks could be classified as catastrophic mortality risk and longevity risk. Catastrophic mortality risk represents the sudden increases in mortality rates. While catastrophic mortality risk describes the shorter lifetime than anticipated of an individual or a group, its counterpart longevity risk represents the uncertain evolution in mortality rates. Catastrophic mortality risk often causes transitory jumps on the mortality curve. Several stochastic mortality models have been developed to capture these jump effects. Due to their low probability and high-impact nature, the timing and the frequency of future catastrophic events and hence mortality jumps are unpredictable, however, the history of events could give information about their future occurrences. In this thesis, a new approach for the modelling of the frequency of catastrophic mortality risk is introduced and a specification of the Lee-Carter model using the renewal process is proposed. Longevity risk is another risk factor that we examined in this thesis. We use index-based longevity swaps to hedge this risk. However, the potential differences between hedging instruments and pension or annuity portfolio cause longevity basis risk. Since the longevity-linked derivatives are traded in the over-the-counter markets, insurers or pension plans can be exposed to counterparty default risk. In this thesis, we provide a hedging framework for longevity basis risk and counterparty default risks in the context of collateralization. Our analysis present that bilateral collateral posting increases longevity basis risk reduction level and hedge effectiveness.