Financial Value-at-Risk Quantitative Analysis: Some Models And Illustrations

The VaR model (Value-at-Risk) has become a mainstream tool of financial Risk measurement and management.With China multi-level capital market system innovation in construction and financial system function gradually consummation, financial risk takes on some new uncertainty characteristics.As far as quantitative analysis and management of financial market risk is concerned, it is very important to use some new methods to quantify the VaR both in theory and practice. To this end, this paper has gathered some existing modeling theory and frontier financial data analysis methods containing GARCH model, Copula function, Wavelet analysis and MCMC algorithm etc. From a multi-scale and bayesian viewpoint and breakthrough points to improve the accuracy of VaR valuation, we try to develop some new risk measurement models and methods at the intersection of statistics, finance and management.Then, through empirical test of some main financial markets and simulation analysis of the models, numerical results effectively support the correctness and feasibility to our models and methods. All in all, the above work enriches the theoretic connotations and practical experiences related to financial risk management and asset optimization.It mainly includes the following distinctive research work and conclusions:Firstly, in order to identify the multiresolution characteristics of VaR, we introduce exchange rate risk into the capital asset pricing model, and get asset pricing model with double factors and the model parameters of wavelet multiresolution estimation method to derive a multiresolution calculation formula for a portfolio VaR and marginal Value-at-Risk (MVaR).it is supported by the result of the empirical analysis to Shanghai A share market. Further analysis indicates China Stock market has multi-scale risk characteristics. Perhaps this is the result of joint effort among the market system risk, the exchange rate risk and heterogeneous investment behavior.Secondly, considering the important influence of the transaction cycle on the volatility characteristics of asset price, this paper introduces the wavelet analysis method into the GARCH modelling theory, and proposes a multi-scale GARCH and multi-scale Augmented-FIGARCH-M model respectively. Through improving the iteration step length, we obtain a numerical algorithm which has better convergence and stability. Conclusions supported by the empirical analysis of Shanghai composite index are that our models can discover the information of multi-time scales contained in the price and capture the volatility characteristics of the VaR in different time scales. The above models help to explore the micro dynamic mechanism of VaR with the transaction cycle evolution.Thirdly, considering the investment behavior, the heterogeneity of asset price and the multi-scale features, the paper introduces wavelet threshold rules into the VaR model, and develops a multiscale estimator for the VaR model using the returns density distribution based on nonlinear wavelet thresholding method.Through the convergence analysis of the valuation acurracy, we found that both the smoothness of the density function space and sample size determine the convergence rate. Finally, via the different sample sizes of simulation experiment of the normal density family, we proved the feasibility of the proposed approach. The model applied to the four stock indexes in china has good practice experience regard to the risk quantitative analysis.Fourthly, in order to quantify the local characteristics of the dependency structure among assets and the influence on the VaR, Wavelet threshold rules are introduced into Copula density estimation. This paper provides a local threshold estimator of the multivariate copulas density. It is shown that three important factors which have effect on the estimation precision are sample size, variable dimension and smoothness index of copula density. The result is supported by the simulation of normal Copula and the empirical analysis. Thus, our methods enhance the local self-adaptation of parametric Copula and help to improve the valuation of VaR and optimization of assets allocation.Fifthly, considering assets return distribution being influenced by the posterior innovation, we propose a time-varying Copula-GARCH-t model assumming the innovation come from standard T-distribution. Using MCMC algorithm to estimate the paramater, we obtain a method to measure a portfolio VaR, and further get the optimal weight of asset allocation Based on risk minimization principle. For the analysis of Shanghai composite index, hang sang index, Taiwan weighted index and s&p 500 index, and our results show that the MCMC method is superior to the classical IFM method. Then we have properly expanded the dependency structure modeling method in the applied scope of financial risk quatitative analysis.Finally, considering the investors risk preference and assuming innovations come from a standard t-distribution, this paper proposes a time-varying Copula-GARCH-M-t model in order to accurately quantify the time-varying dependency structure and forecast portfolio VaR. We design a two-steps MCMC procedure to estimate the model parameter, and obtain one-step prediction of the portfolio VaR. Finally, the example of Shanghai composite index and the s&p 500 index confirms the model and method are effective and feasible respectively. Our models accurately quantify the time-varying characteristics of the two-index dependency structure and the portfolio VaR after the sub-prime crisis.