Long Term Modelling of Economic and Demographic Variables for Risk Assessment of Defined Benefit Pension Schemes

In this thesis, we ascertain the amount of economic capital which Defined Benefit (DB) pension schemes should potentially hold to cover their economic and mortality risks exposures. Recent financial crisis such as the dot com bubble and the 2008 financial crisis has led to funding levels of many DB pension schemes to worsen. Moreover, increasing longevity of pensioners raises further questions on the sustainability of DB pension schemes.

Unlike insurance companies or banks, there is no formal regulatory requirement to quantify the risks of DB pension schemes. Given the increasing uncertainty around the solvency of DB pension schemes, there is an urgent need for such a framework. In this respect, we propose a framework for risk quantification of individual DB schemes across different countries. For our analysis, we focus on three countries; UK, US and Canada.

We implement economic and mortality models to quantify financial risks underlying large DB pension schemes. In particular, we develop an Economic Scenario Generator (ESG) using a graphical modelling approach. We focus on economic variables relevant to pension schemes e.g. price inflation, wage inflation, dividend yield, dividend growth and long term bond yield. The dependence between variables is represented by "edges" in a graph connecting the variables or "nodes". The graphical model approach is fairly easy to implement, is flexible and transparent when incorporating new variables, and thus easy to apply across different datasets (e.g. countries). We also show that the results are consistent with well-established ESGs such as the Wilkie Model in the UK context.

We also compare quantitatively seven stochastic models explaining improvements in mortality rates. In particular, we use the Bayes Information Criteria to choose a model which provides a good fit to mortality data from UK, US and Canada.

We use the graphical model alongside the mortality model to examine the risks of UK, US and Canadian pension schemes. Although the modelling methodology remains the same, we fit the economic and demographic models to data from all three countries.

We then implement our framework to calculate the economic capital for existing and ``stylised" pension schemes.For the UK, we carry out risk assessment of the Universities Superannuation Scheme (USS). For the US, we use a US stylised scheme for our analysis. The US stylised scheme is based on the membership profile and benefits of the USS but adapted to be representative of a US pension scheme. For Canada, we carry out risk assessment of the Ontario Teachers' Pension Plan (OTPP). Both the USS and the OTPP are very large pension schemes with over 300,000 members.

We further carry out sensitivity analysis by varying the mortality assumptions and the asset allocations of the pension schemes. The overall aim of the exercise is to determine and compare the long-term sustainability of pension schemes in different countries.

The interaction between population structure, investments and asset returns will be of interest to pension funds, actuaries and policy-makers, all of whom are interested in the overall health of both public and private pension schemes.