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Research on VaR Estimate Based on HD-estimator

Author: FengXia
Tutor: YangShanChao
School: Guangxi Normal University
Course: Probability Theory and Mathematical Statistics
Keywords: VaR Harrell - Davis estimator Relative deviation Numerical Simulation
CLC: F832.51
Type: Master's thesis
Year: 2009
Downloads: 14
Quote: 0
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Abstract


VaR (Value at Risk) is currently more popular a risk measure VaR concept is simple, easy to understand, easy to operate, can be successfully quantified as a risk, and thus have the world's major banks, investment companies, securities companies and financial regulators of all ages. most of the calculated VaR method assumes that the distribution of income, further modeling. fact, the distribution of financial returns sequence usually presents with a fat tail distribution form more complex, and the distribution is often unknown Therefore, in the process of calculating VaR, often due to improper selection of the model and produce a large error. non-parametric methods do not need to assume that the sequence of return statistical distribution is a distribution method of freedom, which can effectively deal with a sequence of return asymmetric and fat-tail problem, we first discuss the Harrell-Davis estimator (1982) to meet asymptotic properties of alpha-blending and other conditions in the sample, given the speed of its variance, deviation of speed and mean square error obvious positive deviation, overestimation of the phenomenon that is generated by numerical simulation, we found that: k = NP when Harrell-Davis estimates of VaR estimates as equally obvious positive deviation; when k = np, Harrell- Davis estimated the apparent negative deviation. positive deviation and negative deviation, we recommend the use of the weighted estimate as VaR estimates, that is, HDpM = 12 (HDpn p HDpn p 1) the weighted estimated HDpn p positive deviations and HDpn p 1 negative deviation has been good correction to the absolute value of the relative deviation method to estimate the accuracy of the reference standard analysis of three Harrell-Davis estimator in the same sample and the same probability p, kinds of HD VaR estimates HDpn p value, the smallest HDpn p 1, HDPM between the former two HDPM accuracy is significantly better than HDpn p and HDpn p 1, whether it is thin or thick tail tail distribution, the sample is relatively large, the accuracy of the estimates have been greater improvement in the same sample size and the same distribution HDPM relative deviation of both positive and negative, and the absolute value of the relative deviation are relatively small, higher accuracy, which also shows HDPM estimator is relatively stable, relatively good estimated VaR this article on the Shanghai Composite Index and Shenzhen Component Index, a financial index, real estate index, mechanical index and manufacturing index in the January 4, 2007 empirical analysis to 31 December 2008, multi-angle distribution characteristics of their logarithmic yield of rejected day logarithm returns follow a normal distribution assumptions. calculate VaR by Harrell-Davis estimator and Shanghai and Shenzhen risk comparison and risk analysis of four industry analysis results indicate that the risk is greater than the Shanghai Stock Exchange, Shenzhen different industries due to the nature of the industry has a different degree of risk.

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