Application Research On High-dimensional Dynamic Vine Copula For Financial Risks

Development is the theme of economic and social progress,Stability is the premise of development,the government need to forestall and defuse risks to maintain stability.Furthermore,the effective administration of financial risks is extremely urgent.The new Basel Capital Accord emphasizes overall risk management,which requires to think of the multi-dimensional measurement of portfolio risks.Multi dimensional risk does not have the property of sub-additivity.There are nonlinear dependence relations between multi-dimensional risks,and the accurate description of the nonlinear dependence makes the risk measurement more accurate,and is conducive to saving economic capital.Under the circumstances of big data age,modelling of multi-dimensional risks is more important.It is the key of a satisfactory model to describe the non-linear dependence between risks accurately.High-dimensional dynamic vine copula delegates a direction of the frontier research fields.The science nature of modeling and simulation determines the effectiveness of financial portfolio risks measurement.This paper carries out the study just from the above view and the following aspects:First,this paper expoundes systematically the construction methods and steps of high-dimensional dynamic vine copula models,makes the gradual derivation of multi-dimensional simulation process,and solves the application of this method from the perspective of basic theory: During the derivation process,we concentrate on the elaborate display of the fitting process of high-dimensional h dynamic function,and take t copula fuction for example,its correlation parameters follow dynamic AR process.During the fitting process,the construction ranking orders of Pair Copulas are different between C vine and D vine copulas,because the computation methods between the two are different;while in simulation process,the derivation of dynamic h inverse function plays a key role,for the same reason,the computation methods between C vine and D vine copulas are opposite;This part draws pictures of construction and simulation paths of high-dimensional dynamic vine copula,and concludes that the computation methods of C vine and D vine copulas' computation paths and difference between the two.Second,this paper practices the empirical study on risks of stock markets and foreign exchange markets by high-dimensional dynamic vine copula functions,solves the problem of parameters' fitting by two-stage modeling methods,overcomes the non-uniform phenomena of marginal distribution with the extreme theory,computes VaRs through Monte-carlo simulations,backtests risks by UC test,and realizes accurate risk measurement effects.During the process above,the combination between GPD models and high-dimensional dynamic vine copula functions makes research aims reality,as reflects on indepence and uniformality of PIT series and VaR exceedences rationalization.Third,this paper does research on two typical types of C Vine and D Vine,describes the construction and backpushing process of vine structure by means of drawings and formulas,resolves multi-dimensional copula models by the method of vine's picture structure and conditional bi-dimensional copula,and breaks through ‘dimension curse',realized flexibly modeling.This process includes the construction and simulation of high-dimensional dynamic vine copula,and the risk measurement of stock markets and foreign exchange markets.The empirical study results show that this kind of computation method is feasible and efficiency.Fourth,this paper studies vine copula from the perspectives of risk measurement and contagion.In the part of risk measurement,we compare dynamic models to the static ones.While in the part of risk contagion,we take Malaysia Airlines Aircrashes as research objectives,in this process,considering the research efficiency,our study is carried out only by means of static models.During the comparative reseaching process between dynamic and static models,we unsurprisedly conclude that dynamic models perform better than static models.Furthermore,the conclusion before shows that choice of vine type is a key factor in modeling,a wrong type of vine copula function will cause dynamic model to be worse.Fifth,this paper is based on the analysis of multi-dimensional risks measurement with high-dimensional dynamic vine copula,then makes research deeper,analyzes the movement problem of asset portfolio efficiency frontiers and the choice problem of risk asset weights.The conclusion shows that efficiency frontiers of dynamic asset portfolio demonstrates the more rationality and risk aversion and the analysis of marginal VaR proposes that the more USD,the lower risk of foreign exchanges.This paper summarizes previous studies and relevant papers,and makes the following innovations:The first is innovation of study methods.To overcome the problem that a single financial time serie shows the characteristics of skewness,leptokurtosis and fat-tail,the joint distribution of multi-dimensional financial time series may not be an elliptical distribution,the inner correlation is perhaps not linear,and the traditional measurement based on linearity may lead to wrong results,this paper carry out the reseach by high-dimensional dynamic vine copula models during the study process of the risks of foreign exchange makets and stock markets.In the process above,the two-stage modeling method is selected: In the first stage,GJR-GARCH models are used to filter the original series,then GPD models are taken to practise probability integer transform(PIT)of filtered innovation series;In the second stage,PIT series are modeled by dynamic and static vine copulas respectively,the results are compared with each other;While in the reseach of risk contagions from Malaysia Airlines air crashes,SV and vine copula models are combined to realize two-stage models.The second is innovation of study content.This paper takes market risks in Basel Agreement as study objects and portfolio risks measurement of foreign exchange makets and stock markets as study content,and provides a reseach example for fulfilling overall risk management concept in Basel New Capital Agreement.The article provides study prospects on the basis of reseach above:First,The author is restricted by time and strength,only studies risk measurement and contagion problems with high-dimensional dynamic vine copula functions.However,the researches on dynamic hedging and pricing of risk assets are to be practiced;Second,high-dimensional dynamic vine copula may be used to study nature science fields,such as hydrology,tides,electricity,flights,etc,to practise dependence modeling and extreme events forecast,and to solve some skill problems with properties of multi-dimension;Third,the fitting methods of high-dimensional dynamic vine copula can be further optimized,for example: the realization of Bayesian inference of small data,the construction and simulation of high-dimensional dynamic vine copula of discrete data,and the corresponding computation design.