The Research Of Mean-CVaR Model Based On Laplace Distribution

Since 2000 the concept of CVaR was put forward in,CVaR has been considered as a more rational and efficient modern risk management method than the VaR because of its reasonable concept and the superiority in calculation.This paper applies CVaR to portfolio areas,and on the basis of previous researches changes and relaxes some assumptions:capital gains rate obeys Laplace distribution with "sharp peak and thick tail",exchange exists transaction cost,variance-covariance matrix is time varying.Through comparative studying, theoretical and quantitative analysis,this paper establishes a new model and solve it,also studies the impaction of different distribution assumptions,transaction costs and variance covariance matrix to the investment portfolio efficient frontier.First of all,this paper puts forward the concept of Laplace distribution, proves that it does exist "sharp peak and thick tail" comparing with the normal distribution in theory and it is rational to assume Chinese stock market following Laplace distribution.Following,this paper computes CVaR based on Laplace distribution,proves that CVaR based on the distribution of Laplace is larger than it based on normal distribution using numerical calculation.Secondly,this paper theoretically establishes the mean-CVaR model under the relax assumption,obtains explicit solution of the border equation and the global minimum CVaR,and proves that the mouth of boundary line based on Laplace distribution is smaller than the mouth of boundary line based on normal distribution,transaction cost does not affect the mouth of boundary line,receipt corresponding the global minimum CVaR decreases and the risk corresponding the global minimum CVaR increases because of the Laplace distribution and transaction cost,the efficient frontier will parallel move to the lower right corner because of the exchange cost,and the efficient frontier will not only move to the lower right corner but also locate in more below because of the change of distribution.Then,this paper does a lot of detailed,objective,multi-level empirical research to verify the correctness of the conclusions in the theoretical part,and to solve the specific steps of the calculation problem.After it,this paper establishes the dynamic mean-CVaR model based on the time varying variance-covariance matrix,proves that the global minimum CVaR increases but the mouth of boundary line diminishes when one variance of the assets increase,introduces the concept of marginal CVaR and its application in assets adjustment,and then verifies through empirical analysis that China's stock market does exist the phenomena of time varying variance and covariance,as well as the fluctuation to the efficient frontier,illustrates the problem of the calculation and application of marginal CVaR.