The Research And Application Of The Spectral Risk Measure Based On Copula

With the rapid development of financial markets, financial derivatives arebeing constantly updated. The diversified market puts forward higherrequirement for risk measurement. Therefore, the quantitative risk analysis isparticularly important.Based on the introduction of the spectral risk measure theory and riskaversion measure theory, the thesis has provided three forms of risk spectrumincluding hyperbolic risk spectrum and has obtained the SRM estimation,form which the new portfolio optimization model is established. We test thevalidity of the model by using Kupiec, and obtain a practical method tocalculate SRM valuation of single asset and portfolio. The empirical resultsshow that the hyperbolic SRM valuation of a single asset is affected by theconfidence level and risk aversion factor. Under the given confidence level,the SRM and the optimal allocation of the portfolio based on hyperbolic SRMvaluation are influenced by risk aversion factor and expected rate of return.This paper concerns the application of Copula function in SRM valuation,which is an innovation of this paper. Copula function can capture the nonlinear relationship among different assets to improve the accuracy of SRMestimation. When the overall distribution is unknown, we choose the kerneldensity estimation to determine the marginal distribution, and select Copulafunctions to describe the tail dependence. The parameters of Copula functionsare estimated by using the maximum likehood estimation and nonparametricmethods. With the experience function of Copula, we use the square Euclideandistance to evaluate the parameter estimation. At last, a new algorithm basedon Monte Carlo simulation method to estimate SRM is established. Theparameter estimation of five Copula functions, Kendall rank correlationcoefficients and Spearman rank correlation coefficients are calculated. Theempirical results show that there is a strong positive correlation between theShanghai index and the Shenzhen index, and the t-Copula is more suitable forfitting the original data. The algorithm based on Copula-SRM is more accuratethan the traditional SRM algorithm.