Essays on Risk in International Financial Markets

This thesis deals with techniques to model risk in financial markets and consists of four separate essays. The thesis begins with an introduction in chapter one, while chapter two to chapter five contains the four essays. The first essay examines the implication of using various risk measures for portfolio selection. Specifically, three risk measures are examined: variance, Value at Risk (VaR) and Conditional Value at Risk (CVaR). The theoretical properties of these measures are first examined using the theory of stochastic dominance, and it is established that variance and VaR is only consistent with stochastic dominance of first order, while CVaR is consistent with stochastic dominance of second order. In the empirical part of the essay, the optimal portfolios under the various risk measures are examined using stock market data from the US. It is found that although VaR and variance have less attractive theoretical properties, in practice, the difference between the measures is small. Furthermore, a test for stochastic dominance of first and second order is employed. The test suggests that none of the risk measures dominates the others. In the second essay the forecasting performance of GARCH and stochastic volatility models is examined and compared. The results for volatility forecasting is generally quite disappointing, with no model passing the tests for complete unbiased forecasts. The stochastic volatility model delivers in general slightly better forecasts compared to the GARCH model, but the difference is not significant. Moreover, the choice of distribution seems to be unimportant. The VaR forecasts are in general quite satisfying, both for the GARCH model and for the stochastic volatility model. The models are about equally good. Best results are obtained with the student t distribution and skewed student t distribution. The third essay examines various multivariate models for forecasting purposes. A special interest is taken in copulas. Copulas are functions that tie marginal distributions together into a multivariate model. In this essay a new way to incorporate time varying dependence in copulas is suggested and evaluated. Furthermore, alternative time varying as well as constant copulas are also examined, as well as traditional multivariate models. The results suggest that copulas are a valuable tool for VaR forecasting. In the fourth essay, the non-linear dependence between stocks and bonds is examined using a multivariate regime switching model. With the model, each market can, at each point in time, being characterized as being in a high volatility state and in a low volatility state. In a bivariate setting, this corresponds to four separate states. The dependence between the stock market and the bond market is examined across the different states using data from the US, the UK and Japan. It is found for all markets that the dependence is not constant across the regimes. Furthermore, for the US and the UK bond market, it is found that when both the stock market and the bond market are in the high volatility state, the dependence is negative