Longevity: A ‘Simple’ Stochastic Modelling of Mortality

Abstract

All UK insurers exposed to longevity risk need to perform stress tests for their Individual Capital Assessment (ICA). Some have put in place deterministic models which are arguably too simple; others have developed stochastic models that can be demanding and complex.This paper presents a simple model to turn any deterministic mortality scenario into a stochastic model. We propose a simple model of stochastic variation that is easy to explain and to implement, which could be an alternative to and/or complete some of the well known models. The model can be applied to any best estimates of future mortality rates, as it aims to describe how longevity behaves around the projected expected values.The paper proposes a possible calibration on the England and Wales population mortality that produces a minimum indication of possible future variation and uses the results to validate the model's assumptions. Using sample portfolios and the stochastic model, we can simulate cash flows to determine the distribution of the net present values (NPV) of annuity outgo.

Mortality forecasting using a modified Continuous Mortality Investigation Mortality Projections Model for China I: methodology and country-level results

“…There is a clear break at age 30 for males, which is not that significant for females. Both μ and σ are independent of age, especially for ages from 55 to 85, which is consistent with what has been found in Browne et al (2009). As we only have four time points, the normality assumption of X t is easily accepted using Jarque-Bera tests.…”

“…However, one major limitation of the CMI Mortality Projections Model is that it is deterministic. So in this section, we add uncertainties to the best estimates obtained from the CMI approach using techniques outlined by Koller (2011) and described by Browne et al (2009).…”

“…Suppose q x,t is the smoothed (expected) mortality andq x;t is the crude (observed) mortality. Using the model described by Browne et al (2009), we havê…”

“…One major limitation of the CMI Mortality Projections Model is that it is deterministic. However, in this paper, we make it stochastic using techniques outlined by Koller (2011) and described by Browne et al (2009). Comparing this method with a pure extrapolative approach, we find that the CMI approach is more flexible and suitable for long-term mortality forecasting in China.…”

Mortality forecasting using a modified CMI Mortality Projections Model for China II: cities, towns and counties

“…Following the methodology described in Browne et al . (2009), we build stochastic models for cities, towns and counties. It shows that the estimated σ (see section 5 in Huang & Browne, 2014) for males and females is more stable for older ages (55–85), which is consistent with the findings in Huang & Browne (2014) and Browne et al .…”