A financial market model for the US and the Netherlands
This paper describes a capital market model for the Netherlands. This capital market model can be used to evaluate the pension agreement between the government, employers and employees in the Netherlands. Pension funds may invest in a stock market index and in bond funds which rebalance permanently their portfolio to fix the maturity. So we need a description of the stock market and the bond market inclusive the term structure. Both the nominal bonds as well as the development of the stock returns depend on the inflation process which needs to be modelled, too. Net benefits of pensions can be considered as a derivative of bonds and equity, because both the benefits and premiums depend on the investment results. So we need an instrument to evaluate derivative products. The Koijen et al. (2010) model meets all these requirements and will be used after reestimation using Dutch data.
This paper provides a technical documentation of this capital market model and details on the derivations and the estimation. The estimation results are compared to estimates for the US. The results for the Netherlands deviate in several respects from those for the US. In particular, the estimates are less significant. A possible explanation may be that (not included) exchange rate fluctuations are more relevant for Europe than for the US. Due to the small open economy character and the data construction this model can be considered as a model for the north European capital market.
This estimated capital market model will be used to construct scenario sets. These scenarios will be used in an asset liability model (ALM) to evaluate the pension agreement. The Koijen et al. (2010) model is related to Brennan and Xia (2002), Campbell and Viceira (2001) and Sangvinatsos and Wachter (2005). More details of the model can be found in Koijen et al. (2005) and Koijen et al. (2006). A survey of all risks that pension funds are facing, can be found in Broer (2010).
Section 2 presents the model assumptions. The link between nominal and inflation linked bonds is discussed in section 3, just as the term structure. Bond funds implementing constant duration are the subject of section 4. The model is formulated in continuous time, but for simulation and estimation purposes a discretized version is necessary. This discretization is discussed in section 5. To determine the value of derivative products, as for instance pension rights, risk-neutral simulation is used which is discussed in section 6. The data used to estimate the model are discussed in section 7. Section 8 presents the estimation procedure and section 9 the estimation results. The model will be used to generate scenarios. Section 10 presents some possible scenarios to get some feeling for the results. Section 11 concludes.