The United Risk Measurement Of Industries Based On Generalized Hyperbolic Distributions And Copula

In financial market, the risk management is closely related to the distribution of returns. It can be of great benefit to manage risk and reduce loss if we establish a proper model to the joint distribution which will lead to excellent risk management result finally. This paper is based on Chinese stock market. We studied industrial stock price indices in the market, summarized the generalized hyperbolic distribution and Copula theory, constructed multivariate Copula in which GHD were used to fit marginal distributions and carried on the application research in the area of financial market risk."Hyperbolic distribution" gets its name because its density plot behaves like hyperbolic curves after taking logarithm. Which is its superclass, generalized hyperbolic distribution is a kind of distribution family with leptokurtic、skewed and heavy-tailed features. This paper studied the basic concepts、properties、main subclass distributions and parameter estimation methods of generalized hyperbolic distribution. Choosing the industrial indices of real estate industry as an example, we carried on comparative analysis between normal distribution and five subclass distributions of generalized hyperbolic family. According to statistical tests and backtesting results of financial risk management, we selected the most proper distribution model and clarified the merits of generalized hyperbolic family.When it comes to constructing multivariate distributions, Copula theory has natural advantages because it can solve this problem step-by-step by selecting marginal distributions and constructing correlation structures, which is quite flexible and variable. This paper summarized main definitions、theorems、properties and parameter estimation methods of Copula theory. We first choose generalized hyperbolic family as marginal distributions. Then taking Archimedean Copula, specifically, Gumbel Copula, Clayton Copula、Frank Copula, and Elliptical Copula, specifically, Gaussian Copula as models, we carried on the industry correlation analysis of China stock market. After comparing the result from two Copula families, we found that Gaussian Copula given the same result as linear correlation analysis, and it couldn’t measure tail dependence. Thus, we came to a conclusion that Archimedean Copula was more appropriate than Gaussian Copula because it could measure tail dependence. At last, we recognized the top six most related industries of real estate industry from total 27 industries.It needs risk models when measuring market risks. Value-at-Risk is the most common model in practice, but it isn’t a kind of coherent measures because it doesn’t have subadditivity feature. The Basle Committee on Banking Supervision, whos recent action reflects the value of ES theory, has decided to change risk measuring methods from Value-at-Risk to Expected Shortfall gradually in years. Except for these two methods, this paper briefly introduced a more severe one—"Entropic Value-at-Risk" and given its calculation formula based on generalized hyperbolic distribution.For purpose of measuring the united risk of real estate related industries (seven industries in total), it needs to construct high-dimensional Copula structure. This paper solved the problem by using Regular Vines Copula structure with generalized hyperbolic family as marginal distributions. We united a series of 2-dimensional Copulas through R-Vines structure to construct the seven-industry-indices joint daily return distribution. By simulation we got a data set of the joint distribution. Then we computed equal weighted joint daily return and fitted proper generalized hyperbolic distribution to it. At last we calculated VaR. ES and E-VaR based to the distribution we got. Compared to the result of historical data, Copula model got lower risk measure levels. It was consistent with the fact that diversification could reduce risks, according to which we proved that Copula model had more accurate and reasonable result when measuring the united market risk of industries. So the conclusion is. we can take Copula method as one of useful tools when measuring market risk of industries.