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postgraduate thesis: Some topics in correlation stress testing and multivariate volatility modeling
Title  Some topics in correlation stress testing and multivariate volatility modeling 

Authors  
Advisors  
Issue Date  2014 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Ng, F. [伍科俊]. (2014). Some topics in correlation stress testing and multivariate volatility modeling. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5223980 
Abstract  This thesis considers two important problems in finance, namely, correlation stress testing and multivariate volatility modeling.
Correlation stress testing refers to the correlation matrix adjustment to evaluate potential impact of the changes in correlations under financial crises. Very often, some correlations are explicitly adjusted (core correlations), with the remainder left unspecified (peripheral correlations), although it would be more natural for both core correlations and peripheral correlations to vary. However, most existing methods ignored the potential change in peripheral correlations. Inspiring from this idea, two methods are proposed in which the stress impact on the core correlations is transmitted to the peripheral correlations through the dependence structure of the empirical correlations.
The first method is based on a Bayesian framework in which a prior for a population correlation matrix is proposed that gives flexibility in specifying the dependence structure of correlations. In order to increase the rate of convergence, the algorithm of posterior simulation is extended so that two correlations can be updated in one Gibbs sampler step. To achieve this, an algorithm is developed to find the region of two correlations keeping the correlation matrix positive definite given that all other correlations are held fixed.
The second method is a BlackLitterman approach applied to correlation matrices. A new correlation matrix is constructed by maximizing the posterior density. The proposed method can be viewed as a twostep procedure: first constructing a target matrix in a datadriven manner, and then regularizing the target matrix by minimizing a matrix norm that reasonably reflects the dependence structure of the empirical correlations.
Multivariate volatility modeling is important in finance since variances and covariances of asset returns move together over time. Recently, much interest has been aroused by an approach involving the use of the realized covariance (RCOV) matrix constructed from high frequency returns as the expost realization of the covariance matrix of low frequency returns. For the analysis of dynamics of RCOV matrices, the generalized conditional autoregressive Wishart model is proposed. Both the noncentrality matrix and scale matrix of the Wishart distribution are driven by the lagged values of RCOV matrices, and represent two different sources of dynamics, respectively. The proposed model is a generalization of the existing models, and accounts for symmetry and positive definiteness of RCOV matrices without imposing any parametric restriction. Some important properties such as conditional moments, unconditional moments and stationarity are discussed. The forecasting performance of the proposed model is compared with the existing models.
Outliers exist in the series of realized volatility which is often decomposed into continuous and jump components. The vector multiplicative error model is a natural choice to jointly model these two nonnegative components of the realized volatility, which is also a popular multivariate time series model for other nonnegative volatility measures. Diagnostic checking of such models is considered by deriving the asymptotic distribution of residual autocorrelations. A multivariate portmanteau test is then devised. Simulation experiments are carried out to investigate the performance of the asymptotic result in finite samples. 
Degree  Doctor of Philosophy 
Subject  Finance  Econometric models Multivariate analysis 
Dept/Program  Statistics and Actuarial Science 
Persistent Identifier  http://hdl.handle.net/10722/206653 
DC Field  Value  Language 

dc.contributor.advisor  Li, WK   
dc.contributor.advisor  Yu, PLH   
dc.contributor.author  Ng, Fochun   
dc.contributor.author  伍科俊   
dc.date.accessioned  20141125T03:53:13Z   
dc.date.available  20141125T03:53:13Z   
dc.date.issued  2014   
dc.identifier.citation  Ng, F. [伍科俊]. (2014). Some topics in correlation stress testing and multivariate volatility modeling. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5223980   
dc.identifier.uri  http://hdl.handle.net/10722/206653   
dc.description.abstract  This thesis considers two important problems in finance, namely, correlation stress testing and multivariate volatility modeling. Correlation stress testing refers to the correlation matrix adjustment to evaluate potential impact of the changes in correlations under financial crises. Very often, some correlations are explicitly adjusted (core correlations), with the remainder left unspecified (peripheral correlations), although it would be more natural for both core correlations and peripheral correlations to vary. However, most existing methods ignored the potential change in peripheral correlations. Inspiring from this idea, two methods are proposed in which the stress impact on the core correlations is transmitted to the peripheral correlations through the dependence structure of the empirical correlations. The first method is based on a Bayesian framework in which a prior for a population correlation matrix is proposed that gives flexibility in specifying the dependence structure of correlations. In order to increase the rate of convergence, the algorithm of posterior simulation is extended so that two correlations can be updated in one Gibbs sampler step. To achieve this, an algorithm is developed to find the region of two correlations keeping the correlation matrix positive definite given that all other correlations are held fixed. The second method is a BlackLitterman approach applied to correlation matrices. A new correlation matrix is constructed by maximizing the posterior density. The proposed method can be viewed as a twostep procedure: first constructing a target matrix in a datadriven manner, and then regularizing the target matrix by minimizing a matrix norm that reasonably reflects the dependence structure of the empirical correlations. Multivariate volatility modeling is important in finance since variances and covariances of asset returns move together over time. Recently, much interest has been aroused by an approach involving the use of the realized covariance (RCOV) matrix constructed from high frequency returns as the expost realization of the covariance matrix of low frequency returns. For the analysis of dynamics of RCOV matrices, the generalized conditional autoregressive Wishart model is proposed. Both the noncentrality matrix and scale matrix of the Wishart distribution are driven by the lagged values of RCOV matrices, and represent two different sources of dynamics, respectively. The proposed model is a generalization of the existing models, and accounts for symmetry and positive definiteness of RCOV matrices without imposing any parametric restriction. Some important properties such as conditional moments, unconditional moments and stationarity are discussed. The forecasting performance of the proposed model is compared with the existing models. Outliers exist in the series of realized volatility which is often decomposed into continuous and jump components. The vector multiplicative error model is a natural choice to jointly model these two nonnegative components of the realized volatility, which is also a popular multivariate time series model for other nonnegative volatility measures. Diagnostic checking of such models is considered by deriving the asymptotic distribution of residual autocorrelations. A multivariate portmanteau test is then devised. Simulation experiments are carried out to investigate the performance of the asymptotic result in finite samples.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  Creative Commons: Attribution 3.0 Hong Kong License   
dc.subject.lcsh  Finance  Econometric models   
dc.subject.lcsh  Multivariate analysis   
dc.title  Some topics in correlation stress testing and multivariate volatility modeling   
dc.type  PG_Thesis   
dc.identifier.hkul  b5223980   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Statistics and Actuarial Science   
dc.description.nature  published_or_final_version   
dc.identifier.doi  10.5353/th_b5223980   