In Chapter 1, the usefulness of Extreme Value Theory (EVT) methods, GARCH models, and skewed distributions in market risk measurement is shown by predicting and backtesting the one-day-ahead VaR for emerging stock markets and the S&P 500 index. It has been found that the conventional risk measurement methods, which rely on normal distribution assumption, grossly underestimate the downside risk. In Chapter 2, the dependence of the extreme losses of the emerging stock market indices is analyzed. It is shown that the dependence in the tails of their loss distributions is much stronger than that implied by a correlation analysis. Economically speaking, the benefits of portfolio diversification are lost when investors need them most. The standard methodology for bivariate extremal dependence analysis is slightly generalized into a multi-asset setting. The concept of hidden extremal dependence for a multi-asset portfolio is introduced to the literature and it is shown that the existence of such hidden dependence reduces the diversification benefits. In Chapter 3, the mechanisms that drive the international financial contagion are discussed. Trade competition and macroeconomic similarity channels are identified as significant drivers of financial contagion as measured by extremal dependence. In Chapter 4, the determinants of short-term volatility for natural gas futures are investigated within a GARCH framework augmented with market fundamentals. New findings include the asymmetric effect of storage levels and maturity effect across seasons. More importantly, I showed that, the augmentation of GARCH models with market fundamentals improves the accuracy of out-of-sample volatility forecasts.