Financial Market Risk Under The Generalized Hyperbolic Distribution Family

Financial market risk, refer to financial market price factor such asinterest rate, exchange rate,stock price level,etc.to fluctuate causefinancial assets lost possibility.It is one of the most important risks whichthe bank and other financial institutions face in the operational andmanagerial activities How to manage market risk is the joint question thatfinancial institution and academia all focus,so how to measure marketrisk accurately is the key.Until now, Value at risk or VaR has become thepreferred tool to measure market risk among several kinds of tools.VaR issimply the worst possible reture(which is possible a loss)of an asset orportfolio with a given confidence level and a given holding period underthe normal market condition.According to VaR's definition we can see VaR is a nothing but aquantile analysis,which accuracy depends on the hypothesis of returndistribution.Normal distribution was usually suggested to model financialtime series in many studies,but it is a pity that many studies indicate thatnormanl distribution can't describe the fat tail of most financial timeseries.In this paper, we try to improve the accuracy of the risk assessmentfrom drawing into a new hypothesis of return distribution. Many studies abroad indicate that the generalized hyperbolic distributions can provideexcellent fits to empirically observed return distributions.In this paper wediscuss the application of GH distribution to risk measurement in Chinesestock market,in order to estimate GH distribution we follow the EMalgorithm framework of McNeil for GH distributions and we use EMalgorithm.To evaluate the fit of the generalized hyperbolic distributionswe use AD statistic and FOF statistic which pay more attention to the tailsof the distribution and therefore hints at the possibility to model theprobability of extreme events,then we utilized simulations to get betterresults for the GH distributions than for the normal distribution.Then wedram GH distributions into VaR method to compute VaR of ShanghaiStock exchange,here as same as the volatility, the quantile varies as timepasses,so we use different quantile,and use GARCH models to estimatethe volatility to get VaRs.Finally we list the result of backtesting of thismodel based on the hypothesis of GH distributions, comparing to otherdistributions and other VaR methods, obviously the model based on theGH distributions can provide better evaluation to the empirical VaR ofShanghai Stock Exchange,especially for small levels of probability, thanthe normal distribution and other methods.