Research On Time-varying Risk Measurement And Application Of Highdimensional Portfolio Based On GAS-factor Copula Model

With the in-depth development of the global financial market,complex financial products emerge one after another,and the interrelationships between products and markets have become closer.The outbreak of the U.S.financial crisis in 2008 caused chaos and panic in the global market.Financial institutions and investors suffered huge losses.It also demonstrated the fact that the close relationship between financial products and the market is enough to detonate huge systemic risks.Before the 2008 financial crisis,Wall Street used Gaussian copula to price CDOs,but ignored the relevance of the collective decline in housing prices across the United States,which warned us of the importance of choosing the right model and reducing the risk of the model.In the context of the gradual and in-depth development of my country's economy and society,the interdependence and mutual influence between financial markets are getting closer and closer.The price synergy of financial assets makes the fluctuations or risks of the whole or part of the financial market in a region quickly spread,Infecting and magnifying markets in other regions,the two stock market crashes in 2015 and 2018 have further aroused people's attention.Research on the relevance and risk of the financial field has gradually become the focus of research for researchers.As an important part of the financial market,the stock market determines its important position in correlation research and risk management.There are often linkage effects between stocks,between industries,between sectors,and between different markets.A fall or rise in the price of a stock or sector often causes the prices of other stocks or sectors to fall or rise.The contagion of this volatility makes the price fluctuations of an asset affect the fluctuations of other assets and even the entire market.When it changes,this related structure has been changing.Research on the relevance of assets in various financial fields plays a very important role in the construction of asset portfolios and investment risk management.The Copula model is an important tool for studying related structures.Copula theory was first proposed by statistician Sklar in the 1950 s and is mainly used in the field of probability and statistics.As the correlation between markets or assets in the financial field becomes closer and more complex,the Copula theory is gradually introduced into the financial field to describe the complex related structure of the financial market.Embrechts(1999)is the pioneer of introducing the Copula model into the financial field,and it uses the Copula model to measure the correlation between return rate series.Rockinger(2001)and Jondeau(2006)used the CopulaGARCH model to study the correlation between financial indexes.Scholars have extended the basic Copula model to the dynamic Copula model and the highdimensional Copula model in the state dimension and space dimension,respectively,to describe the dynamic dependence and high-dimensional variable dependence between variables.The generalized autoregressive score(GAS)model proposed by Creal(2012)can be used to describe the dynamic edge distribution.Nevertheless,the domestic application of the copula model is still mainly focused on the description of the relationship between binary variables.The research on the vine copula with dynamic characteristics also mainly studies the low-dimensional field.Therefore,the dynamic factor copula model is used to move the research object to the high-dimensional field.Expansion will help deepen the research on investment portfolios and provide useful references for investors and regulators.The main problem studied in this paper is the portfolio risk analysis under the dynamic factor copula model.First of all,we need to make the assumption of marginal distribution of the marginal return of assets.After considering the autoregressive,thick and asymmetrical tail distribution phenomena of asset returns in the real world,as well as the leverage effect of the stock market,this article chooses AR(1)-EGARCH(1,1)-partial t model constructs the marginal distribution of stock returns.Then we need to make assumptions about the specific form of the factorial copula model.This article introduces the GAS-factor Copula model to conduct an empirical study on the daily return data of the stocks of 40 listed companies.The model fitting is divided into two steps.The first step is to use the maximum likelihood method to fit the AR-EGARCH model on the marginal distribution of each stock;the second step is to achieve the standardization after the marginal distribution is fitted.The new information is converted into copula observations,and the MCMC algorithm is used to sample each group of copula model parameters.Investigate the characteristics of the correlation structure between stocks;and select the most effective model by comparing the measurement effects of different copula models on portfolio risk.This article is divided into the following parts: The first chapter is the introduction.The content of this chapter is the research background,research significance,research content,research methods and innovations of this article.The second chapter is a literature review,combing copula model,portfolio theory and VaR value at risk theory from five aspects.The third chapter is the research design,introduced the marginal distribution and copula model construction process,and their respective parameter estimation methods.The fourth chapter is an empirical analysis.In this chapter,after selecting stock portfolios and descriptive statistics,sampling is used to obtain estimates of the parameters of the copula model,and further based on the model sampling results to examine the characteristics of the posterior correlation coefficients between the sub-asset variables.Finally,based on the model constructed above,different models are used to calculate the VaR of the investment portfolio composed of index stocks,and the accuracy of the risk characterization of different models is compared.The fifth chapter is divided into three parts.Firstly,it summarizes and analyzes the previous article and draws research conclusions.Next,policy recommendations are made on the basis of empirical analysis.Finally,it is to make an outlook on the future research direction.The main conclusions of this paper are:(1)The stock samples selected in this paper have obvious volatility clustering and ARCH effects.According to the fitting results of the EGARCH model,the value of is significantly non-zero,that is,there is a significant leverage effect.When the yield is negative When it hits,it will have a greater impact on the volatility of new interest.(2)There are significant differences in the factor copula model parameters of different industries.The dynamic grouping factor copula model can introduce more parameters to control the tail correlation of different types of assets.Compared with the ungrouped model,the grouping model incorporates more sample information.The characterization is more precise.(3)After sampling the model parameters,the Monte Carlo simulation method is further used to calculate the posterior Kendall rank correlation coefficient between stock returns.Taking steel stocks and electronic stocks as examples,the investigation found that the two are falling in the stock market.,Faced with the stock market crash,the correlation coefficient rose significantly.(4)Use different time-varying factor copula models to estimate the future risk of the investment portfolio and backtest the VaR value.The three factor copula models of Gauss,student t,and GSt include grouping and ungrouping respectively.The results show that the risk measurement effect of all grouping models is better than that of ungrouping models;models with parameters that control skewness have better performance than A model without a skewness parameter is good.The innovations of this article are reflected in:(1)The previous research on the copula model mainly focused on the correlation between two or several markets and two or several assets,and the use of the Copula model to study high-dimensional problems is rare.The Fuji copula model can analyze high-dimensional variables by disassembling high-dimensional variables into a combination of several twodimensional variables,but once the dimensionality continues to grow,the calculation will become very complicated;this article introduces the factor copula model to use latent variables As a medium,it can characterize the interdependent structure of high-dimensional variables relatively efficiently.The factor copula model is used to investigate and analyze the relevance of sub-assets in highdimensional investment portfolios,and is applied to portfolio risk management.The estimation accuracy of VaR is used to determine the factor copula model suitable for my country's stock market.This is a high-dimensional investment portfolio management.Useful to try.(2)In the process of model construction,this article combines the AR-EGARCH model with the partial t-factor Copula model,and assumes that the factors obey the dynamic GAS model.The current domestic research on dynamic copula mainly involves the variable structure rattan copula model,which reflects the structural changes of the copula model itself;while the GAS-factor Copula model uses autoregressive scores to enable factor loading to dynamically change over time,thereby reflecting The time-varying nature of the inter-variable dependency structure adds to the empirical research experience of dynamic copula.(3)In the research on the related structure of high-dimensional portfolios,the introduction of more copula model parameters by industry grouping to control the tail-related movement between assets can make the model's description of the asset-related relationships more comprehensive and reduce the single The factor copula model has fewer parameters and insufficient description of complex correlations.The better performance of the grouped copula model is also conducive to investors and regulators to better understand the different related structures presented by different types of assets,thereby generating useful guidance for practice.The shortcomings of this paper are mainly reflected in the following two points:(1)This paper uses the GAS model to generate dynamic factor loads driven by observations,thereby building a time-varying factor copula model.However,in the process of using the model,it did not consider whether the form of the model itself should have phased changes.(2)The model set in this article is a dynamic single factor copula model,that is,the number of latent variables is one.After the asset dimension continues to increase,a single factor may not be enough to explain the correlation between multiple assets.