Browsing by Author "Njenga, Carolyn"
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- ItemLongevity risk and the econometric analysis of mortality trends and volatility(Social science research network, ) Njenga, Carolyn; Sherris, MichaelLongevity risk and the modeling of trends and volatility for mortality improvement has attracted increased attention driven by ageing populations around the world and the expected financial implications. The original Lee-Carter model that was used for longevity risk assessment included a single improvement factor with differential impacts by age. Financial models that allow for risk pricing and risk management have attracted increasing attention along with multiple factor models. This paper investigates trends, including common trends through co-integration, and the factors driving the volatility of mortality using principal components analysis for a number of developed countries including Australia, England, Japan, Norway and USA. The results demonstrate the need for multiple factors for modeling mortality rates across all these countries. The basic structure of the Lee-Carter model can not adequately model the random variation and the full risk structure of mortality changes. Trends by country are found to be stochastic. Common trends and co-integrating relationships are found across ages highlighting the benefi ts from modeling mortality rates as a system in a Vector-Autoregressive (VAR) model and capturing long run equilibrium relationships in a Vector Error-Correction Model (VECM) framework.
- ItemLongevity risk modelling with application to insurer longevity risk based capital stress marginsNjenga, CarolynFuture mortality rates are uncertain and the risk that estimated mortality rates will be higher than observed rates has negative financial implications for providers of living benefit ts including life annuities and pensions. This thesis studies time trends and cohort trends in mortality rates to determine the number of factors that drive mortality changes. An econometric analysis of mortality improvements is used to give a clearer picture of the stochastic nature of mortality rates in a lower dimensional data space as this thesis uses co integration analysis for dimension reduction.A multi-country analysis of standardized mortality rates fi nds evidence of stochastic trends and a signifi cant number of common factors. However, no evidence of common stochastic trends is found. An analysis of Australian mortality rates establishes there are non-stationary and stationary mortality rates by age. The common stochastic trends across age-groups which are exhibited within the Australian data lead to the characterization of mortality rates using a stochastic trend model. Dimension reduction is performed using the Heligman and Pollard (1980) parametric mortality model. The trends in the data are reflected using flexible Vector Autoregressive (VAR) models allowing for correlation between the estimated Heligman and Pollard model parameters. Bayesian Vector Autoregressive (BVAR) models which additionally quantify parameter risk are shown to signifi cantly improve the forecast accuracy when fi tting the developed HP-BVAR model to data from 1946-1995 and then comparing its out-of-sample forecasts to observed data from 1996-2007 for Australian mortality rates. Allowing for parameter uncertainty shows it to be a signi cant component of total risk since the results are realistic probabilistic forecasts. The HP-BVAR model is applied to the calibration of the longevity stress margin of the life insurance capital charge. The structure and magnitude of the current simpli fication by APRA result in a longevity stress margin that is found to be too prudent and too generalised. An alternative age-dependent simpli fication is proposed.
- PublicationModeling mortality with a bayesian vector autoregression(ARC Centre of Excellence in Population Ageing, ) Njenga, Carolyn; Sherris, MichaelMortality risk models have been developed to capture trends and common factors driving mortality improvement. Multiple factor models take many forms and are often developed and fitted to older ages. In order to capture trends from young ages it is necessary to take into account the richer age structure of mortality improvement from young ages to middle and then into older ages. The Heligman and Pollard (1980) model is a parametric model which captures the main features of period mortality tables and has parameters that are interpreted according to age range and effect on rates. Although time series techniques have been applied to model parameters in various parametric mortality models, there has been limited analysis of parameter risk using Bayesian techniques. This paper uses a Bayesian Vector Autoregressive (BVAR) model for the parameters of the Heligman-Pollard model and fits the model to Australian data. As VARmodels allow for dependence between the parameters of the Heligman-Pollard model they are flexible and better reflect trends in the data, giving better forecasts of the parameters. Forecasts can readily incorporate parameter uncertainty using the models. Bayesian Vector Autoregressive (BVAR) models are shown to significantly improve the forecast accuracy of VAR models for mortality rates based on Australian data. The Bayesian model allows for parameter uncertainty, shown to be a significant component of total risk.