Copula-GARCH Model Based On Extreme Value Theory And Its Applications In Finance Risk

The relationship of the financial markets has been researched a lot in the past period of time. Because the Copula model takes into account not only the degree of correlation between financial time series, also consider which has become an important tool to study the field of financial risk related structures.Copula function with a single in practical applications, it is difficult to fully characterize the correlation pattern between the financial markets, it is to construct a more flexible Copula function, in order to better describe the complex structure of financial markets or the correlation between the stock. Take full account of the different characteristics of the different Copula function, select the different characteristics Copula functions are grouped together in some way, the formation of new Copula functions-mixed the Copula function of (M-on Copula). A relatively single Copula function to build the most important advantages of the M-Copula, that can contain different types of M-Copula can measure the degree of correlation between the variables relevant parameters, while the linear combination coefficients that weight can capture dependency structure of the different mode. And mixed Copula choose different Copula to create structure relative to a single Copula, a better description of the true correlation structure.Since the distribution of financial asset returns have significant fat tail, so will underestimate the tail of the normal distribution assumption extreme risk. Extreme value theory for modeling data tail, it does not need to assume that the distribution of assets and income, but with the data directly fitting the tail of the distribution, and can capture the probability of extreme events, extreme value theory in the measure of high confidence The degree of risk shows unique advantages.January4,2002to2012, the Shanghai Industrial Index, Business Index and the index of the three sectors of the public exponent sequence we select2666sets of data for empirical analysis. Fitting the GARCH model for each index series to describe the marginal distribution, use extreme value theory to improve the end of the data, select the Archimedean Copula function Gumbel Copula, Clayton Copula and Frank Copula to construct the M-Copula model. From which you can see:(1) the use of the POT model in the extreme value theory to improve the marginal distribution, making the risk assessment closer to the real.(2) The combination of M-Copula model and Monte Carlo simulation of the VAR is effective, a single structure Copula will underestimate the true risk. This shows that the mixed Copula more realistic response to the potential of the structure.