Macrofinancial risk has become increasingly important over time as global markets have become increasingly more connected. In this paper we apply several econometric measures of connectedness based on Granger-causality networks to the changes of sovereign risk of European countries and credit risks of major European, U.S., and Japanese banks and insurers to investigate the evolution of these connections. This allows us to calculate the extent of connections between financial institutions and sovereigns and quantify the effects of risk transmission within and across countries and financial institutions. The recent global financial crisis that began in 2007 reminds us about the importance of including complex interactions, spillovers, and feedback relationships between financial institutions and sovereigns in the modeling and analysis of financial crises and sovereign risk. We examine how vulnerabilities can build up and suddenly result in a financial crisis with potentially disastrous feedback effects for sovereign debt and economic growth. Traditional macroeconomic analysis overlooks the importance of financial system risk, which makes it ill-suited to examine interconnectedness and transmission mechanisms in response to common shocks. Using contingent claims analysis (CCA) and network theory, we propose new ways to measure and analyze financial system, sovereign, and credit risks.