由於死亡率曲線與殖利率曲線同樣可用水平(level)、斜率(slope) 、曲度(curvature)來描述，且兩者之參數皆為受到時間因素影響之動態因子，故本研究應用Nelson-Siegel(1987)系列之動態利率期間結構模型，如Diebold and Li (2006)的三因子模型，針對日本1947至2006年死亡率進行配適，再以自我相關模型檢視因子的趨勢變化進而預測；結果發現本研究所使用模型在配適死亡率曲線上效果良好，而高齡人口死亡率預測上較幼年、青少年人口精確，以日本資料而言Svensson四因子模型相較於Lee-Carter模型預測能力佳，但在年輕人口死亡率中則不然。

The main purpose of this study is tempting to extend existing model in interest model context to mortality modeling. Since the mortality curve has resemblance of interest rate yield curve. Both of them can be describe by level, slope, and curvature terms. Also, the parameters of two curves are the function of time. We apply the Nelson and Siegel family yield rate models such like Diebold and Li (2006) model to fit and forecast the mortality term structure. By using the Japanese mortality data within 1947 to 2006, we find out that the fitting of these models are precise, especially when age dimension being truncated to age 20-103. The forecasting performances comparing with the benchmark Lee-Cater model is better in elder age but worse in younger age.

Cairns, A.J.G., Blake, D., Dowd, K.(2006). A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk & Insurance.

Diebold, Francis X. and Canlin Li, 2006, “Forecasting the Term Structure of Government Bond Yields,” Journal of Econometrics, Vol. 130, 337-364.

Dowd, K., Cairns, A.J.G., Blake, D., Coughlan, G.D., Epstein, D., and Khalaf-
Allah, M. (2008) Evaluating the Goodness of Fit of Stochastic Mortality Models
", Forthcoming, Pensions Institute Discussion Paper PI-0803.

Dowd, K., Cairns, A.J.G., Blake, D., Coughlan, G.D., Epstein, D., and Khalaf-Allah,
M.(2008)Backtesting Stochastic Mortality Models: An Ex-Post Evaluation of
Multi-Period-Ahead Density Forecasts", Forthcoming, Pensions Institute Discussion
Paper PI-0802.

Jens H. E. Christensen, Francis X. Diebold, Glenn D. Rudebusch. (2008).An Arbitrage-Free Generalized Nelson-Siegel Term Structure Model

Lee, R.D., Carter, L. R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association 87 (419), p.659-675.

Lewis (1982). C.D. Lewis Industrial and business forecasting methods, Butterworths, London (1982).

Nelson, C and A Siegel. Parsimonious modeling of yield curves. Journal of Business,
Jan 1987.

Renshaw, A and Haberman,S.(2006). A cohort-based extension to the lee{carter model for mortality reduction factors. Insurance Mathematics and Economics.

Svensson, Lars E. O. (1995) “Estimating Forward Interest Rates with the Extended Nelson-Siegel Method,” Quarterly Review, No. 3, Sveriges Riksbank, 13-26

Wong-Fupuy, C. Haberman, S. (2004). Projecting Mortality Trends: Recent Developments in the United Kingdom and the United States

Willets,R. (2004). The cohort effect: insights and explanations - Actuarial Journal, Vol. 10, No. 4., pp. 833-877

余清祥、曾奕翔(2005)，Lee-Carter模型分析:台灣地區死亡率推估之研究，2005年台灣人口學會學術研討會論文。

陳文琴(2008)，｢死亡率改善模型的探討及保險商品自然避險策略之應用｣，政治大學風險管理與保險學系碩士論文