A Hierarchical Model of Tail-Dependent Asset Returns
This chapter introduces a multivariate stochastic model for logarithmic asset returns which accounts for such stylized facts as skewness and excess kurtosis of the marginal probability distributions of asset returns and tail dependence of their joint distributions. The model is derived by evaluating initially independent Brownian motions, grouped by sectors, at the sector-specific stochastic chronometers. This stochastic time represents the irregular information flow relevant for doing business in the respective sector. As the companies in different sectors may also not be entirely independent of one another, the sector-specific stochastic chronometers are themselves evaluated at an independent common stochastic chronometer that represents the flow of general information relevant for all firms in the market, such as changes in the overall macroeconomic conditions.*†
The specific time-change procedure described is a novelty of my approach. To the best of my knowledge, the first example of utilization of a two-stage stochastic time change in order to generate multidimensional Lévy processes with a hierarchical dependence structure. The model’s hierarchical structure has the advantage of allowing for a stronger dependence within given economic or geographic sectors or certain sub-portfolios as compared to a weaker dependence between the sectors/sub-portfolios. Moreover, the magnitude of sector-specific ...