Research of Multivariate Volatility Financial Assets Models

When analyzing the movements of the financial assets prices is important to assess, build and predict the dynamics of volatility and profitability of the instruments. This problem can be accomplished with using Multivariate GARCH models. Development of Multyvariate GARCH models can be seen as a great breakthrough on "the curse of dimensionality" in financial modeling. These models can be applied to the asset pricing process, in the process of diversification in portfolio theory, in evaluating of risk and in risk-management – wherever you want to analyze the volatility of assets or accompanying volatility of several instruments or markets. In the diploma explores not only simple models used to predict the covariance, but also more complex, perhaps the most effective, working sets of methods for modeling and forecasting of financial time series, for example BEKK model and DCC model, which is one of the most recent and very successful approaches in the family of multivariate GARCH-models. The work includes the developed approach to modeling Multivariate-GARCH based on not a simple classical volatility formula, but using volatility estimator by Kunitomo ("Bridge-estimator") with the proof of its efficiency in relation to estimators by Garman-Klass and Parkinson. The application by the example of stock prices of the largest Russian oil companies for the last 10 years is the a few results on the evaluation of return of assets. In the diploma the program module in MATLAB has been designed which allows use these models on real data.