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The Lee–Carter (LC) model, developed in the early 1990s, is internationally used for mortality rate projection and risk evaluation. When the LC model is applied to Japanese death rates, however, the residuals of the logarithm of age-specific death rates reveal a time series correlation, and “undulation” is observed in the residual phase on the age and year axes. Previous studies point out the possibility of a cohort effect in Japanese death rates, and one proposes a modified LC model incorporating the death deferred factor. In this paper, taking previous studies into account, we analyze the residual structure involved in the application of the LC model to Japanese death rates and propose the LC-VAR (LC Vector Autoregressive) model, which is an extended LC model, based on this analysis. In addition, we demonstrate examples of the application of the LC-VAR model to pension liability valuation and pricing single net premiums as well as cover the key points in mortality projections.

Analysis of the Residual Structure of the Lee–Carter Model: The Case of Japanese Mortality