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**A Parametric Factor Model of the Term Structure of Mortality.** / Haldrup, Niels; Rosenskjold, Carsten Paysen T.

Research output: Working paper/Preprint › Working paper › Research

Haldrup, N & Rosenskjold, CPT 2018 'A Parametric Factor Model of the Term Structure of Mortality' Institut for Økonomi, Aarhus Universitet, Aarhus.

Haldrup, N., & Rosenskjold, C. P. T. (2018). *A Parametric Factor Model of the Term Structure of Mortality*. Institut for Økonomi, Aarhus Universitet. CREATES Research Papers No. 2018-06

Haldrup N, Rosenskjold CPT. 2018. A Parametric Factor Model of the Term Structure of Mortality. Aarhus: Institut for Økonomi, Aarhus Universitet.

Haldrup, Niels and Carsten Paysen T. Rosenskjold *A Parametric Factor Model of the Term Structure of Mortality*. Aarhus: Institut for Økonomi, Aarhus Universitet. (CREATES Research Papers; Journal number 2018-06). 2018., 26 p.

Haldrup N, Rosenskjold CPT. A Parametric Factor Model of the Term Structure of Mortality. Aarhus: Institut for Økonomi, Aarhus Universitet. 2018 Jan 15.

Haldrup, Niels ; Rosenskjold, Carsten Paysen T. / **A Parametric Factor Model of the Term Structure of Mortality**. Aarhus : Institut for Økonomi, Aarhus Universitet, 2018. (CREATES Research Papers; No. 2018-06).

@techreport{a0aa85f379d640d9ac49cc6f6410fc92,

title = "A Parametric Factor Model of the Term Structure of Mortality",

abstract = "The prototypical Lee-Carter mortality model is characterized by a single common time factor that loads differently across age groups. In this paper we propose a factor model for the term structure of mortality where multiple factors are designed to influence the age groups differently via parametric loading functions. We identify four different factors: a factor common for all age groups, factors for infant and adult mortality, and a factor for the {"}accident hump{"} that primarily affects mortality of relatively young adults and late teenagers. Since the factors are identified via restrictions on the loading functions, the factors are not designed to be orthogonal but can be dependent and can possibly cointegrate when the factors have unit roots. We suggest two estimation procedures similar to the estimation of the dynamic Nelson-Siegel term structure model. First, a two-step nonlinear least squares procedure based on cross-section regressions together with a separate model to estimate the dynamics of the factors. Second, we suggest a fully specified model estimated by maximum likelihood via the Kalman filter recursions after the model is put on state space form. We demonstrate the methodology for US and French mortality data. We find that the model provides a good fitt of the relevant factors and in a forecast comparison with a range of benchmark models it is found that, especially for longer horizons, variants of the parametric factor model have excellent forecast performance.",

keywords = "Mortality Forecasting, Term Structure of Mortality, Factor Modelling, Cointegration",

author = "Niels Haldrup and Rosenskjold, {Carsten Paysen T.}",

year = "2018",

month = jan,

day = "15",

language = "English",

series = "CREATES Research Papers",

publisher = "Institut for {\O}konomi, Aarhus Universitet",

number = "2018-06",

type = "WorkingPaper",

institution = "Institut for {\O}konomi, Aarhus Universitet",

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TY - UNPB

T1 - A Parametric Factor Model of the Term Structure of Mortality

AU - Haldrup, Niels

AU - Rosenskjold, Carsten Paysen T.

PY - 2018/1/15

Y1 - 2018/1/15

N2 - The prototypical Lee-Carter mortality model is characterized by a single common time factor that loads differently across age groups. In this paper we propose a factor model for the term structure of mortality where multiple factors are designed to influence the age groups differently via parametric loading functions. We identify four different factors: a factor common for all age groups, factors for infant and adult mortality, and a factor for the "accident hump" that primarily affects mortality of relatively young adults and late teenagers. Since the factors are identified via restrictions on the loading functions, the factors are not designed to be orthogonal but can be dependent and can possibly cointegrate when the factors have unit roots. We suggest two estimation procedures similar to the estimation of the dynamic Nelson-Siegel term structure model. First, a two-step nonlinear least squares procedure based on cross-section regressions together with a separate model to estimate the dynamics of the factors. Second, we suggest a fully specified model estimated by maximum likelihood via the Kalman filter recursions after the model is put on state space form. We demonstrate the methodology for US and French mortality data. We find that the model provides a good fitt of the relevant factors and in a forecast comparison with a range of benchmark models it is found that, especially for longer horizons, variants of the parametric factor model have excellent forecast performance.

AB - The prototypical Lee-Carter mortality model is characterized by a single common time factor that loads differently across age groups. In this paper we propose a factor model for the term structure of mortality where multiple factors are designed to influence the age groups differently via parametric loading functions. We identify four different factors: a factor common for all age groups, factors for infant and adult mortality, and a factor for the "accident hump" that primarily affects mortality of relatively young adults and late teenagers. Since the factors are identified via restrictions on the loading functions, the factors are not designed to be orthogonal but can be dependent and can possibly cointegrate when the factors have unit roots. We suggest two estimation procedures similar to the estimation of the dynamic Nelson-Siegel term structure model. First, a two-step nonlinear least squares procedure based on cross-section regressions together with a separate model to estimate the dynamics of the factors. Second, we suggest a fully specified model estimated by maximum likelihood via the Kalman filter recursions after the model is put on state space form. We demonstrate the methodology for US and French mortality data. We find that the model provides a good fitt of the relevant factors and in a forecast comparison with a range of benchmark models it is found that, especially for longer horizons, variants of the parametric factor model have excellent forecast performance.

KW - Mortality Forecasting, Term Structure of Mortality, Factor Modelling, Cointegration

M3 - Working paper

T3 - CREATES Research Papers

BT - A Parametric Factor Model of the Term Structure of Mortality

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -