The Measurement of Spatial Effects in Multivariate Volatility Models

<p>The idea of time-dependent conditional variance provides the basic of contemporary financial management. It&rsquo;s widely accepted nowadays that assets&rsquo; volatilities affect each other, and besides the interacting assets may belong to different industries. Multivariate volatility models are based on this fact. It allows them estimate volatility more accurately, than separate univariate models. This resulted in the increase of decision-taking effectiveness in such field as asset pricing, portfolio management, insurance and risk management.</p><p>The master thesis is devoted to the multivariate volatility models estimation and studying the aspects of volatility and covolatility modeling subject to sectorial interdependence between assets in the portfolio.</p><p>The master thesis is aimed at application of ideas from spatial econometrics, particularly spatial matrices, in multivariate volatility modeling.</p><p>Among the goals of the master thesis are learning the basics of spatial econometrics, a Monte Carlo simulation for evaluation of estimator performance, estimation of spatial multivariate volatility models on real data, measuring the volatility spatial effects inherent to Russian stock market.</p><p>One of the main difficulties in estimation multivariate volatility models is their computational complexity. The relevance of this thesis is in the fact that spatial multivariate volatility models do not only substantially decrease the number of parameters to estimate, but also allow to measure and analyze the spatial effects of volatility.</p><p>&nbsp;&nbsp;To estimate the sectorial interdependence between assets, in other words, spatial effects, we derive three spatial specifications for such models as BEKK, GO-GARCH and CCC. The three specifications are homogeneous, group homogeneous and heterogeneous. Spatial specifications allow to divide the volatility transmission into two types: direct through conditional variance and indirect through conditional covariances. The research shows that for twenty Russian assets under consideration in all three models the direct transmission dominates. This means that conditional covariance has smaller impact on portfolio volatility than conditional variance.</p><p>The master thesis resulted in the following:</p><p>&bull;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Three spatial specifications are derived for three multivariate volatility models: BEKK, GO-GARCH and CCC.</p><p>&bull;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The Monte Carlo simulation demonstrates evidence of good performance of estimator.</p><p>&bull;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The volatility of portfolio, consisting of fourteen Russian stocks from four industries, is estimated using the three spatial specifications for three models.</p><p>&bull;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; According to goodness-of-fit criteria spatial specifications are in most cases outmatch original specifications of BEKK, GO-GARCH and CCC.</p><p>&bull;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; According to goodness-of-forecast criterion BEKK model outperforms the other models in both spatial and original specifications.</p><p>The master thesis can be expanded by completing the above mentioned goals for other multivariate volatility models, to be more exact, models of dynamic correlations and equicorrelations. It enables to resolve the &ldquo;curse of dimensionality&rdquo; problem in these models and estimate the effects of spatial spillovers between assets.</p>