Hierarchical clustering of market risk models

Abstract: This thesis aims to discern what factors and assumptions are the most important in market risk modeling through examining a broad range of models, for different risk measures (VaR0.01, S0:01 and ES0:025) and using hierarchical clustering to identify similarities and dissimilarities between the models. The data used is daily log returns for OMXS30 stock index and Bloomberg Barclays US aggregate bond index (AGG) from which daily risk estimates are simulated. In total, 33 market risk models are included in the study. These models consist of unconditional variance models (Student's t distribution, Normal distribution, Historical simulation and Extreme Value Theory (EVT) with Generalized Pareto Tails (GPD)) and conditional variance models (ARCH, GARCH, GJR-GARCH and EGARCH). The conditional models are used in filtered and unfiltered market risk models. The hierarchical clustering is done for all risk measures and for both time series, and a comparison is made between VaR0:01 and ES0:025.  The thesis shows that the most important assumption is whether the models have conditional or unconditional variance. The hierarchy for assumptions then differ depending on time series and risk measure. For OMXS30, the clusters for VaR0:01 and ES0:025 are the same and the largest dividing factors for the conditional models are (in descending order): Leverage component (EGARCH or GJR-GARCH models) or no leverage component (GARCH or ARCH) Filtered or unfiltered models Type of variance model (EGARCH/GJR-GARCH and GARCH/ARCH) The ES0:01 cluster shows that ES0:01 puts a higher emphasis on normality or non-normality assumptions in the models. The similarities in the different clusters are more prominent for OMXS30 than for AGG. The hierarchical clustering for AGG is also more sensitive to the choice of risk measure. For AGG the variance models are generally less important and more focus lies in the assumed distributions in the variance models (normal innovations or student's t innovations) and the assumed final log return distribution (Normal, Student's t, HS or EVT-tails). In the lowest level clusters, the transition from VaR0:01 to ES0:025 result in a smaller model disagreement.