This thesis consists of three papers analysing time-varying cross-border correlation and spillover risk. Existing literature has devoted significant resources to quantify these two types of risk within a variety of markets and asset classes. The implications of these studies have great importance in policy making, securities trading and in commercial banking activities. In the aftermath of the recent financial crisis dynamic risk related topics have gained a renewed interest. This thesis aims to bridge gaps in the currently available research. "Dynamic Stock Market Covariances in the Eurozone" is a joint work with Professor Gregory Connor. This paper examines the short-term dynamics, macroeconomic sensitivities, and longer-term trends in the variances and covariances of national equity market index daily returns for eleven countries in the Euro currency zone. We modify Colacito, Engle and Ghysel’s Mixed Data Sampling Dynamic Conditional Correlation GARCH (MIDAS-DCC GARCH) model to include a new scalar measure for the degree of correlatedness in time-varying correlation matrices. We also explore the robustness of the findings with a less model-dependent realized covariance estimator. We find a secular trend toward higher correlation during our sample period, and significant linkages between macroeconomic and market-wide variables and dynamic correlation. One notable finding is that average correlation between these markets is lower when their average GDP growth rate is lower or when more of them have negative GDP growth. "Correlation Dynamics in the G7 Stock Markets" explores the changing magnitude of synchronised equity index return correlations within the G7 stock markets in response to dynamic variation in the economic environment and secular trends toward greater capital market integration. The full sample period is split into "pre-crisis" and "crisis" periods. The empirical results show that the G7 markets exhibit a significant positive trend toward higher cross-border correlations over the full sample period and that there is significant time-series autocorrelation in the magnitude of cross-market return correlations. These findings are consistent for both periods. Correlation magnitude seems to behave differently during the "pre-crisis” and “crisis” periods in relation to the business-cycle-related effect and the turbulence of the financial markets. During the "crisis" period the average correlation between these financial markets is lower during quarters when more of them have negative GDP growth or when their average GDP growth is lower. The reverse holds for the "pre-crisis" period. Also, the positive relationship between the correlation magnitude and stock market variance is only present in the “crisis” period. We argue that during the crises periods, financial markets are strongly influenced by local factors. "Directional Spillovers in Banks’ Credit Default Risk and Related Variables" analyses the total and directional spillovers across carefully selected variables directly related to the credit risk of financial institutions: bank CDS spread, real estate market index, interest rate term spread, interbank liquidity spread and national stock market index, using daily data from 1st of January 2004 to 31st of December 2012. The spillover analysis is undertaken within five European Union countries: core countries France and Germany, periphery countries Spain and Italy, and a reference country, the UK. A multiple structural break estimation procedure is employed to detect sudden changes in shock transmission. The directional spillover framework reveals complex dynamics between the CDS spreads and credit risk related variables. The national stock markets show a clear leading role in shock transmission across selected variables; whereas the role of other variables in sample is reversed during the course of the crisis. The real estate index is found to be mostly affected by country specific events; and the shock transmission of the interest rate term spread and the interbank liquidity spread differs for the UK and the Eurozone countries.