Hedging Longevity Risk for Life Insurance Companies
Date Issued
2008
Date
2008
Author(s)
Tsai, Jeffrey Tzu-Hao
Abstract
The longevity impacts human sociality including insurance companies and individuals. The demand for annuity product increase rapidly for individuals but issuing the annuity-type product pushes the insurance company in extreme high longevity risk. This risk is systematic and non-diversifiable by the Low of Large Number method. We provide two new methods to against this risk by the concept of nature hedging of annuities and life insurances. On is the Duration Match approach, another is Quantile Liability Allocation (QLA) approach. Both strategies reduce the longevity risk effectively and provide the insure companies with an optimal liability allocation at the same time.n Part I, we hedge annuity product risk with life insurance and find the optimal hedging proportion under Duration Match approach. Different to Cox and Lin (2007) swap approach, the proportion formula is derived by effective duration and has an analytic formulation. The mixed proportions under different age, gender, coverage and method of payment are explored numerically. Part II incorporates the mortality nature hedging strategy of Cox et al. (2007) and the two-factor stochastic mortality model of Cairns et al. (2006b). We propose a quantile liability allocation (QLA) method for insurance companies to hedge against mortality systematic risk. We integrate the risk premiums loadings of systematic risk into the model by Sharpe Ratio Pricing Principle suggested as Milevsky et al. (2006). The QLA model can lead to an optimal liability structure that has smaller quantiles under the required loading return and a multiple liabilities framework. We compare the hedging results to duration match method of Wang et al. (2008) and show that QLA method have a better distribution risk reduction effect when the mortality shift are non-parallel. The parameter uncertainty could be included into the model as well.
Subjects
mortality systematic risk
liability allocation
longevity risk
duration match
natural hedge
parameter risk
SDGs
Type
thesis
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