Pricing Longevity Risk Based On Stochastic Mortality Model

With the improvement of people’s living standards and health conditions, the mortality rate of the Chinese population keeps declining, the average life expectancy showing the extension of the trend, which leads to the age structure of Chinese population gradually shifts aging. The aging population makes the pension payment level exceed original expectation of plan providers, which initiate longevity risk.Longevity risk is kind of systemic risk; pension plan providers deserve the risk premium return for bearing such risk. So an important prerequisite for a pension plan provider to avoid and manage longevity risk is rationally measure and pricing it. However, the current pension annuity product pricing method still regards the fixed mortality as actuarial assumptions, did not take the stochastic change and dynamically improve of mortality into account. So life expectancy will cause annuity payments rates to be underestimated, the pension plan providers suffer financial distress. So it is necessary to take reasonable measure to model and pricing it. Therefore, the research and discussion of longevity risk modeling and pricing has important theoretical and practical significance.The accurate forecast of change in the future mortality data is an important longevity risk measurement basis, consider the historical mortality data is limited in China, this paper improves the traditional Lee-Carter model, uses empirical mortality data to fit and forecast, gets ideal results. Taking longevity risk inherent in individual annuity products as measure object, based on the mortality prediction data, adjusts existing annuity table to include dynamic improvement of mortality, analyzes the longevity risk impact on individual annuity actuarial present value and interest rate sensitivity. The results show life insurance company faces the risk of annuity products underpricing. Then the paper introduces the Wang Transform to pricing longevity risk. The results show that the market price of individual annuity pure single premium includes a longevity risk premium return, and market price of longevity risk decrease with the increase of the insured age. At the end of this paper, proposes viable suggestions to manage longevity risk: the use of a more accurate mortality model and promptly revised life table, amend the actuarial model of annuity present value to include longevity risk impact, modify the design of annuity products policy, establish a reasonable mortality index, vigorously develop the Chinese financial derivatives market especially mortality index derivatives market, etc..