High-Dimensional Stress Test And MVCAViaR Model With Applications To Financial Risk Management

Stress tests and Value-at-Risk(Va R)are two common tools in financial risk management.Stress tests can be used to model the impacts of potential extreme events on the stability of the financial system.Va R,on the other hand,describes the maximum loss that a portfolio can suffer at a given confidence level.Both risk management tools have attracted the attention of domestic and overseas financial regulatory organizations.Existing stress testing methods are often based on(generalized)linear regression,(structural)vector autoregression or DCC-GARCH models,but these methods cannot simultaneously depict the high-dimensional,dynamic and nonlinear relationships in the financial market.Meanwhile,a multivariate conditional autoregressive Va R model(MVCAVia R)is proposed to model the joint Va Rs of different financial markets,but this method cannot be extended to high-dimensional cases due to the curse of dimensionality.In this paper,we propose a new DHDC stress testing method based on the dynamic high-dimensional copula model.Compared with the existing stress tests,our new method depicts the high-dimensional dynamic nonlinear relationship among different individuals,rather than the static two-dimensional linear correlation.The relationship is high dimensional because individuals not only directly relate to each other,but also influence one another through a third party.We consider a dynamic relationship as risks change over time.It has become a well-known fact that different financial markets have a non-linear relationship.In addition,our DHDC stress test method can allow more diverse stress test scenarios and the calculation of any statistics of the dependent variables,such as the expectation,variance,quantile(Va R)and expected shortfall(ES),in each scenario.Many of the previous stress testing methods,on the other hand,can only consider the impact of a particular shock and calculate only one statistic,such as expectation.Furthermore,our method utilizes the publicly available market data to construct a daily mark-tomarket framework of stress test,and as a result,it can depict the changes of systemic risk under a particular shock based on constantly updated market information.In this paper,we also solve the curse of dimensionality problem for MVCAVia R model.MVCAVia R model can depict the tail risks and tail dependencies of different financial assets at the same time.Therefore,it is widely used to study the spillover effects of tail risks among financial assets.Being suitable for multiple time series in theory,it also faces the curse of dimensionality problem in practical application: when the number of cross sections increases,the number of parameters will increase in square term.The estimation of too many parameters leads to over-fitting,poor prediction accuracy and difficult interpretation of the interdependence.To solve this problem,we propose a new LASSO-MVCAVia R model.By applying LASSO to the MVCAVia R model in a novel way,we effectively impose a restriction on the number of parameters of the model,so that one can estimate the restricted MVCAVia R model conveniently.Both the Monte Carlo simulations and the empirical analyses show that the LASSO-MVCAVia R model is superior to the bivariate MVCAVia R and the high-dimensional unconstrained MVCAVia R model in terms of prediction accuracy and goodness of fit.When the number of parameters exceeds the number of observations,our method can still get parameter estimates as our LASSO procedure restricts the number of non-zero parameters to be less than the number of observations.Another theoretical contribution of this paper is that we propose a new systemic risk measure conditional market value loss(Co MVL).Most of the existing risk measures only contain return information,such as Va R and ES.Another risk measure,SRISK,also uses quarterly data such as capital adequacy ratio and liabilities besides daily return data.Due to different data frequencies,one needs to simulate daily data of several months in the future when estimating SRISK,which affects the reliability and effectiveness of the measure.In this paper,we propose a new risk measure Co MVL,which has the nice properties of the existing risk measures Co ES and MES,and adds the market value information of the same frequency in its definition.As a result,it can better measure the impact of negative shocks.Our method has many applications.In Chapter 3,we apply DHDC stress test to studying the impact of shocks of real estate industry on other 17 industries in China.As the real estate industry can directly affect one industry,as well as indirectly affect the industry through other industries,we distinguish the direct and indirect impacts of the real estate industry shock by setting different stress test scenarios.Furthermore,we set up a complex network of risk spillover according to the size of direct influence among industries,so that we can identify the path of risk transmissions among industries.At the same time,we set up a specific stress scenario to identify the intertemporal effect of shocks of real estate industry,i.e.,the impact of a negative shock of the real estate industry in the first week on other industries in the first,second,third and fourth weeks after the shock.Our empirical analyses show that,the real estate industry shock has a great adverse impact on the Co MVL of manufacturing,finance,information technology,leasing business and wholesale and retail industries,and a small impact on culture and sports,education and accommodation and catering industries.Meanwihile,the direct impact of real estate industry shock on an industry is obviously less than the indirect impact and the real estate industry shock has a negative impact on manufacturing and financial industry through seven industries.In addition,the impact of real estate industry on the Co MVL of various industries will weaken over time,but this phenomenon is heterogeneous among different industries,with manufacturing,finance and information technology industries lasting longer.In Chapter 4,we apply the newly proposed LASSO-MVCAVia R model to studying the spillover effects of the tail risks of different international stock markets.Previous studies on the transmission of extreme risks between stock markets mostly focus on two countries,which ignores the indirect impact caused by the interrelation of international stock markets,and tends to underestimate the probability and loss of extreme risks in stock markets,especially in crisis times.In this chapter,we examine the 13 important stock markets in the world,including G7 countries,BRICS countries and China's Hong Kong.Compared with two-dimensional or highdimensional MVCAVia R models,the LASSO-MVCAVia R model can better depict the complex correlation structure of international stock markets,and thereby avoiding the underestimates of the market risk and impulse responses.We find that the Chinese stock market has obvious two-way spillover effects with the stock markets of the United States,France,Germany,Japan,China's Hong Kong,Canada and India.Quantile impulse responses show that China,India,Russia and China's Hong Kong,Japan and Italy have a lower contribution to the spillover effects of tail risk of international stock markets.The United States,France,Germany,Britain and Canada have a greater contribution to the spillover effects of tail risk of international stock markets.In Chapter 5,we analyze the risk spillover effects among China's exchange,Treasury bonds,commodity futures,financial futures and stock markets by a highdimensional MVCAVia R model.The Wald test based on the MVCAVia R model and the backtesting analyses show that there are significant risk spillover effects among the five markets in crisis or prosperity periods.At the same time,we use the stress test to find that the short-term impact of a single market shock will be absorbed by other financial markets,but the combined shock of four financial markets will reduce(increase)the lower left tail(higher right tail)quantile of the stock market by 1 percentage point.In addition,we find that currency market and stock market can realize mutual hedging of volatility and crash risks,while stock market and Treasury bond market can realize mutual hedging of volatility risk but not crash risk.With the financialization of the commodity futures market,stock market can hedge the volatility and crash risks of the commodity futures market,but the commodity futures market cannot hedge the volatility or crash risk of the stock market.This paper has made both some methodological and empirical contributions.For the methodological parts:(1)We propose a new DHDC stress test method,which can measure the impact of extreme shock more accurately by simutaneously capturing the high-dimensional,dynamic and nonlinear relationship among individuals.(2)We solve the curse of dimensionality problem of the MVCAVia R model.(3)We propose a new systemic risk measure Co MVL,which can better depict the impact of a shock.Our empirical contributions include:(1)We systematically analyse the impacts of negative real estate industry shocks on all other industries in China,not only the direct impacts but also the indirect impacts.We also establish a complex network of risk spillover according to the size of direct influence among industries,so that we can identify the path of risk transmissions among industries.(2)We set up a high-dimensional LASSO-MVCAVia R model to analyze the risk spillovers among G7,BRICS and China's Hongkong stock markets,which helps us better understand the international stock markets risks faced by China.(3)We analyze in details the comoving effects of the stock,foreign exchange,bond,futures and other financial markets in China in crisis,normal and boom states,as well as the hedging of volatility and crash risks among different financial markets.