The impact of parameter uncertainty in insurance pricing and reserve with the temperature‐related mortality model

Abstract

Changes in mortality rates have an impact on the life insurance industry, the financial sector (as a significant proportion of the financial markets is driven by pension funds), governmental agencies, and decision makers and policymakers. Thus the pricing of financial, pension and insurance products that are contingent upon survival or death and which is related to the accuracy of central mortality rates is of key importance. Recently, a temperature‐related mortality (TRM) model was proposed by Seklecka et al. (Journal of Forecasting, 2017, 36(7), 824–841), and it has shown evidence of outperformance compared with the Lee and Carter (Journal of the American Statistical Association, 1992, 87, 659–671) model and several others of its extensions, when mortality‐experience data from the UK are used. There is a need for awareness, when fitting the TRM model, of model risk when assessing longevity‐related liabilities, especially when pricing long‐term annuities and pensions. In this paper, the impact of uncertainty on the various parameters involved in the model is examined. We demonstrate a number of ways to quantify model risk in the estimation of the temperature‐related parameters, the choice of the forecasting methodology, the structures of actuarial products chosen (e.g., annuity, endowment and life insurance), and the actuarial reserve. Finally, several tables and figures illustrate the main findings of this paper.

Mortality effects of economic fluctuations in selected eurozone countries

“…Growth of the aging population is evidence for a positive milestone of society's well-being. Holders of longevity risk, particularly now, need to be more mindful of their funding and price methods to ensure their products are priced and reserved sufficiently (Richards & Currie, 2009;Seklecka, Pantelous, & O'Hare, 2018). For instance, life expectancy for European countries has risen significantly over the past few decades.…”

“…Each country experiences a different trend of longevity improvement (Pampel, 2005;Yang & Wang, 2013). It helps the government in funding pension policies sufficiently, actuaries and insurers in pricing age-related financial instruments appropriately and individuals in planning their post-retirement favorably (Godinez-Olivares, Boado-Penas, & Pantelous, 2016;Richards & Currie, 2009;Seklecka et al, 2018). Life expectancy rose by 14 years from 1950 to 2015 (see the trend in longevity has produced a new curve to standard life expectancy, causing current life tables to underestimate future life expectancy (Barrieu et al, 2012).…”

“…As in previous studies (e.g., Niu & Melenberg, 2014;Seklecka, Pantelous, & O'Hare, 2017, 2018, our forecasting methodology is a combination of explanation and extrapolation methods (Booth & Tickle, 2008; see Section 2 for more details). As in previous studies (e.g., Niu & Melenberg, 2014;Seklecka, Pantelous, & O'Hare, 2017, 2018, our forecasting methodology is a combination of explanation and extrapolation methods (Booth & Tickle, 2008; see Section 2 for more details).…”

“…This phenomenon has become more crucial since it has drawn the attention of many organizations such as pension funds and life and health insurers, and also individuals. Holders of longevity risk, particularly now, need to be more mindful of their funding and price methods to ensure their products are priced and reserved sufficiently (Richards & Currie, 2009;Seklecka, Pantelous, & O'Hare, 2018). The government faces challenges in financing an aging population with longer lifespans while insurers are liable for providing conducive and appropriate healthcare solutions, and need to understand expected lifetimes sufficiently.…”

“…Thus the need to model mortality more accurately becomes critical in planning for one's sustainability. It helps the government in funding pension policies sufficiently, actuaries and insurers in pricing age-related financial instruments appropriately and individuals in planning their post-retirement favorably (Godinez-Olivares, Boado-Penas, & Pantelous, 2016;Richards & Currie, 2009;Seklecka et al, 2018).…”