Application Research Of Optimized Model Based On Copula In Finance

Optimization is a topic that people have been discussing and passionate about all over the world,involving all aspects of human social life.The optimization model is a model which established to solve the existing optimization problems by using mathematical knowledge.With the continuous acceleration of the global economic and financial diversification and integration process,the global financial market has become intricate and complicated.Therefore,it has become a hot topic to establish an optimization model in complex financial markets,and portfolio theory as the beginning of quantitative finance,how to optimize in portfolio theory has attracted more attention.It has been almost 70 years since the portfolio theory was proposed.During the70-year research process,the early research directions mainly focused on risk measurement.The researchers didn't begin to focus on the distribution of asset variables until the value at risk and the condition value at risk were successively proposed.The traditional portfolio theory model assumes that each asset variable obeyed a normal distribution.But with the deepening of the research,the researchers found that the actual financial asset variables didn't obey the normal distribution,so they introduced the copula function.This article mainly studies the interdependence of financial market assets and how to allocate the optimal weights among the assets on the basis of introducing the copula function.First,the research background,research process,research steps,relevant basic knowledge are introduced on the basis of querying and reading the existing literature,and the mean-CVa R portfolio optimization model with transaction costs is proposed as well.Then,use the Dow Jones Industrial Average,Nikkei 225,FTSE 100,Shanghai Composite Index,India BSE30 Index and Hang Seng Index as the research objects,the R-vine copula was established to study their respective in the pre-COVID-19(2010.1.4-2019.12.30)And during the COVID-19(2019.12.31-2021.1.15)the dependence and its dependency changes,the parameters estimation uses the semi-parametric estimation method.Among them,the optimal marginal distribution is established for each stock index in each period.Research shows that the optimal marginal distribution of different data in different periods is different,and it is unreasonable to establish the same marginal distribution for all data.The analysis of the results shows that the dependence between the FTSE 100 Index and the Dow Jones Industrial Average is the strongest in these two periods.Secondly,in these two periods,the FTSE 100 Index connects Asia and America.However,the outbreak of the COVID-19 changed the tail dependence between the indexes,making the dependence between the indexes changed from a non-zero symmetrical tail dependence to a strong lower tail dependence,indicating that during the COVID-19,there is a strong risk of contagion among the various indexes studied.In addition,the outbreak of the COVID-19 has also weakened the dependence between the Hang Seng Index and the FTSE 100 Index,while the dependence between the India BSE30 Index and the FTSE 100 Index has increased.Finally,the daily closing prices of the six stock indexes during the entire period(2010.1.4-2021.1.15)are used as the research object to calculate the investment weight.First,Convert the daily closing prices into daily logarithmic returns,establish the daily returns of each index separately Optimal "typical fact" model and marginal distribution,built R-vine copula to analyze the dependent structure,use IFM to estimate R-vine copula parameters.Then use the established optimal model,marginal distribution,R-vine copula structure and corresponding parameters to simulate the future rate of return,use this rate of return to model the mean-CVa R model and the mean-CVa R model with transaction costs.Finally,the results of the equal-weight combination,the minimum risk combination and the optimal weight combination under a given return of the two models at the 95%confidence level are obtained.The research results show that establishing the portfolio optimization model and calculating the optimal investment weights can effectively control investment risks.Comparing the optimal weight combination risk under the same expected return of the mean-CVa R model and the mean-CVa R model with transaction costs can be found,when the expected return is less than the return of the minimum risk combination,the optimal weight combination of model with transaction costs will reduce investment risk;when the expected return is greater than the return of the minimum risk combination,ignoring transaction costs will make the risk of the optimal weight combination underestimated.