High-dimensional Dependence Modelling for Cross-market Analysis

University of Technology Sydney. Faculty of Engineering and Information Technology.In the age of information explosion, data mining and machine learning techniques have been dramatically involved in financial market modelling. Many scholars have shown the significance of dependence modeling across financial markets, especially the catastrophic global financial crisis (GFC) in 2008. The sharp fluctuations across different markets demonstrated the dependence is high-dimensional, contains various hierarchical and horizontal relationships, and often presents complicated dependence structures and characteristics such as asymmetrical structure and tail dependence. Thus, a good understanding of cross-market dependence is of great importance in cross-market applications such as portfolio management and risk management. Unfortunately, modeling the dependence across financial markets is very challenging. Typical approaches including Markov models, probabilistic graphical models and neural network models could take the advantages by building conditional dependence structures between random variables to resolve the high dimensional issues. However, these models always impose unrealistic assumptions (e.g., Gaussian or its mixtures), which fail to capture the complex dependence structures in the real world. At the same time, the copula has been demonstrated effective in presenting dependence between variables in statistics and finance communities. By splitting the joint distribution into the dependence between variables and the independent marginal distributions, copula provides a flexible mechanism to investigate the specifications of the dependence across the market and the marginal distributions independently. Nevertheless, building effective dependence structures to address the above complexities still significantly challenges existing copula approaches. Based on the above research limitations and challenges, this thesis addresses the following changes: (i) the cross-market dependence structure is often embedded with strong and complicated coupling relationships on high dimensionality as with any complex behavioural and social systems; (ii) financial variables such as daily return have been shown to follow non-Gaussian distributions, which means dependence models should cover a wide range of dependencies in order to capture the asymmetric dependencies; and (iii) various tail dependencies such as lower and upper tail dependence is ubiquitous in financial markets. We propose weighted partial D vine copula, weighted partial regular vine copula and weighted regular vine variational LSTM models for high-dimensional cross-market modeling. All above approaches for the high dimensional cross-market dependence modeling are applied in accordance with business applications, such as Value at Risk. These models not only provide insightful knowledge for investors to control and reduce the aggregation risk of the portfolio, but also show promising potential for further exploration and development in cross-market analysis and applications