Modeling and pricing longevity derivatives using Skellam distribution

• Published in: Insurance, mathematics & economics mathematics & economics, 2021-07, Vol.99, p.341-354
• Main Authors: Kung, Ko-Lun, Liu, I-Chien, Wang, Chou-Wen
• Format: Article
• Language: English
• Subjects: Death & dying; Derivatives; Estimating techniques; Heavy tail; Iterative methods; Longevity; Longevity swaps; Maximum likelihood estimation; Maximum likelihood method; Missing data; Mortality; Mortality forecasting; Mortality modeling; Mortality rates; Poisson distribution; Skellam distribution; Studies; Volatility
• ISSN: 0167-6687; 1873-5959
• DOI: 10.1016/j.insmatheco.2021.04.002

•This paper derives the mortality improvement based on the Skellam distribution, the difference of two Poisson death counts.•We provide the iterating estimators of the model parameters from maximum likelihood estimation.•We demonstrate the risk in mortality improvement has a non-linear effect on the swap premium with respect to maturity. We propose a novel mortality improvement model with the difference of death counts follows the Skellam distribution. We extend Mitchell et al. (2013) by considering the difference in Poisson death counts instead of the ratio of subsequent mortality rate, which does not have a known distribution. We derive the iterative estimators of the model from the Skellam distribution. Our model can employ maximum likelihood estimation for estimation issues such as missing data and provides a better fit than Mitchell et al. (2013). Using English and Wales mortality rate age 0-89 data during 1950-2016, the model estimate suggests that the age-dependent mortality improvement is slower than the benchmark, which coincides with a recent observation by Office for National Statistics (2018). The forecasting performance outperforms the Poisson and M10 model. We make inferences on the price of longevity swaps and analyze how the volatility shock of mortality improvement affects the premium of longevity swaps.