Spectral Risk Measures Of Financial Market Based On Kernel Density Estimation

As the current risk measurement of financial institutions and an important tool of management, Value at Risk (VaR) is the most concise form of the asset portfolio of the potential probability. The risk management and control reflects its unique advantages, which have been widely used. Nevertheless, VaR there are many bad points. VaR in practice the theory still has some limitations, mainly in the following aspects:(1) VaR risk measurement methods do not have to be the sub-additivity; (2) the objective function of VaR The programming problem is generally not convex programming, the local optimal solution is not necessarily the global optimal solution; (3) VaR only provide a certain confidence level the maximum expected loss of assets, it can not reflect more than the value once the extent of possible loss; (4) lack of information on the description of the tail.Now solve the problem of estimating VaR methods, including numerical approximation, extreme value theory and Monte Carlo simulation methods, but these methods generally rely on changes in the underlying market risk factors obey normal (Gaussian) distribution assumptions, but experience shows that market data compared to the assumptions of normal distribution with a fat tail characteristics, and thus this phenomenon will directly lead to "short incident" the possibility of being underestimated. In this paper, nonparametric kernel density estimation method, the reaction can be more accurate financial data, "fat tail" of that character.Spectral risk measure to the profit and loss distribution of portfolio investors, the specific shape and combination of subjective risk aversion, is the same risk measure, and has convex, that is a finite number of convex combination of spectral risk measure is still a spectral risk measure, it is reasonable effectively measure the financial risks of a possible choice.This paper describes the definition by the value at risk, the advantages and limitations of theory, based on coherent risk measure by introducing the framework and the spectrum of risk measured by the formation of the spectrum of risk measurement techniques and nuclear density estimation method, introduced into the financial market risks measuring, and according to law of large numbers using Monte Carlo simulation method, the complex density function of the sub-bit point estimates, combined with financial risk spectrum and some basic features of the discrete spectral risk measure the approximate form, to gain a risk measure for spectral analysis and practical method of calculation. Thus, spectral risk measure of financial market risk measurement and portfolio optimization problem for both of practical and theoretical value.