Mortality surface by means of continuous time cohort models

Abstract

We study and calibrate a cohort-based model which captures the characteristics of a mortality surface with a parsimonious, continuous-time factor approach. The model allows for imperfect correlation of mortality intensity across generations. It is implemented on UK data for the period 1900-2008. Calibration by means of stochastic search and the Differential Evolution optimization algorithm proves to yield robust and stable parameters. We provide in-sample and out-of-sample, deterministic as well as stochastic forecasts. Calibration confirms that correlation across generations is smaller than one.

Longevity Risk Management and the Development of a Value-Based Longevity Index

“…Our correlation matrix therefore is based on a fixed calendar time and a fixed time horizon with mortality rates for the differing cohorts observed through time. This differs from the instantaneous cohort correlation structure of Jevtic et al (2013), which fixes the initial age at 40 for all cohorts.…”

“…The calibration results in Jevtic et al (2013) appear unrealistically high; the correlation matrix is constant and independent of the initial age; and the calibrated parameters result in large out-of-sample forecasting errors for old ages (age 80 and beyond). The high correlations appear to result from the common factor, which introduces high dependence across cohorts.…”

“…In the age-period affine mortality model of Blackburn and Sherris (2013), perfect correlations across multiple cohorts are implicitly assumed. The work in Jevtic et al (2013) notes that empirically, cohort correlations are imperfect and attempts to capture this property with their cohort-based affine mortality model. They use a two-factor Ornstein-Uhlenbeck process to calibrate the mortality surface, with a common factor for all cohorts and a cohort-specific factor.…”

“…Motivated by Jevtic et al (2013), we develop a cohort model with more realistic correlations. The calibration results in Jevtic et al (2013) appear unrealistically high; the correlation matrix is constant and independent of the initial age; and the calibrated parameters result in large out-of-sample forecasting errors for old ages (age 80 and beyond).…”

“…Since the drift and diffusion coefficients are age-independent, the model is unable to produce a richer, initial age-dependent correlation structure. We address these issues and develop an improved cohort-based model motivated by Jevtic et al (2013).…”