Scenario Generation for Asset and Liability Management Models Applied to a Saudi Arabian Pension Fund

Abstract

In Asset and Liability Management (ALM) models, there are parameters whose values are not known with certainty at decision time, such as future asset returns, liability and contribution values. Simulation models generate possible “scenarios” for these parameters, which are used as inputs in the optimisation models and help thus in making decisions. These decisions can be evaluated in the sample, on the same scenarios that were used for making the decision, and out-of-sample, on a different, usually much larger, scenario set. With asset return simulation, the major difficulty lies in the multivariate nature of the data. We propose to capture this via the historical copula, making thus no distributional assumptions. We suggest the use of univariate sample generation which allows for different asset returns to be modelled by different distributions. The liabilities and contributions values have as a main source of uncertainty the population numbers; we propose to model this by adapting a model used in biology (BIDE). We use the resulting scenario generator in four different ALM optimisation models, using a dataset from the largest Saudi Arabian pension fund and the Saudi Arabian market index.