Graphical models and variational Bayesian inference for financial networks - Xin, Luyin (2019)
After the 2008 financial crisis, researchers found it’s necessary to understand the financial market as a network of institutions where connections among participants play an essential role in the contagion of systemic risk. To learn financial networks, network models based on correlations are superior but have limited modeling power. In this thesis, we propose a more powerful framework of graphical models, which is applicable to monoscale, multiscale and time-varying cases with sparse graphical representation. Existing frequentist methods for learning graphical models need to tackle penalty parameter selection while here we provide a tuning-free variational Bayesian inference by approximating the intractable posterior distribution by the variational distribution. It imposes shrinkage priors on the off-diagonal elements of the precision matrix, approximates the posterior distribution of the precision by Wishart distribution and then employs natural gradient-based optimization. The objective of multiscale model is to capture long-range correlations between distant sites while the time-varying graphical model aims to obtain smoothly-evolving networks across time. Simulated data is used to compare the performance of our models with other frequentist approaches. It shows that our models can better recover the true graph with fewer parameters and less computational time. Then we apply models to infer financial networks during the 2008 financial crisis period and the result reveals that monoscale model can detect connections within each region while multiscale model detects centricity and vulnerability in the system by removing the regional effect. On the other hand, the time-varying model successfully captures the market turbulence during the financial breakdown. Each of them is helpful to provide certain insight about the financial system.