Stochastic Correlation and Portfolio Optimization by Multivariate Garch

Modeling time varying volatility and correlation in financial time series is an important element in derivative pricing, risk management and portfolio management. The main goal of this thesis is to investigate the performance of multivariate GARCH model in stochastic correlation forecast and apply theses techniques to develop a new model to enhance the dynamic portfolio performance in several context, including hedge fund portfolio construction.\\ First, we examine the performance of various univariate GARCH models and regime-switching stochastic volatility models in crude oil market. Then these univariate models discussed are extended to multivariate settings and the empirical evaluation provides evidence on the use of the orthogonal GARCH in correlation forecasting and risk management performance when an equally weighted portfolio is considered. \\ The recent financial turbulence exposed and raised serious concerns about the optimal portfolio selection problem in hedge funds. The dynamic portfolio construction performance of a broad set of multivariate stochastic volatility models is examined in a fund of hedge fund context. It provides further evidence on the use of the orthogonal GARCH in dynamic portfolio constructions and risk management. \\ Further in this work, a new portfolio optimization model is proposed in order to improve the dynamic portfolio performance. We enhance the safety-first model with standard deviation constraint and derive an analytic formula by filtering the returns with GH skewed t distribution and OGARCH. It is found that the proposed model outperforms the classical Mean-Variance model and Mean-CVAR model during financial crisis period for a fund of hedge fund.Ph.D