The Report of the Research Working Party on Correlations and Dependencies Among All Risk Sources (Part 4): Serial Correlations of Interest and Inflation Rates

This chapter discusses an approach to model the value of an outstanding, discounted liability under the impact of uncertain interest and inflation rates. Interest and inflation rates are modeled separately as time series to take into account autocorrelation. Subsequently, the dependence between interest and inflation is modeled using copulas. The goodness of fit of some copulas can be evaluated on the basis of historic data using a quantile plot. This is done for the Gumbel, Clayton and basis of historic data using a quantile plot. This is done for the Gumbel, Clayton and Independent copulas. The Gumbel copula, which gives the best fit, is then compared with the Normal copula to show that the two copulas are very similar with the parameters chosen. The distribution of the required reserve is shown under four different copula assumptions: comonotonicity, which represent the best case, countermonotonicity which represents the worst case, and the Gumbel and Normal copulas which represent more realistic scenarios. The choice of copula has considerable impact on the higher percentiles of the required reserve, and the adopted approach is effective in selecting a suitable copula.