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Estimation of VaR Using Copula and Extreme Value Theory

Author: LiFang
Tutor: ZuoLi
School: Changchun University of
Course: Applied Mathematics
Keywords: Extreme Value Theory Copula Function Portfolio Model VaR
CLC: F830.9
Type: Master's thesis
Year: 2011
Downloads: 100
Quote: 0
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Abstract


In the correlation analysis of financial activities has a very important significance, such as investment portfolio, asset pricing and risk analysis, and other issues are used in correlation analysis. At present the correlation between variables method, and they are the linear correlation coefficient method and causal analysis. Copula theory is the second application of the method. It is a new measurement tool, Copula function of risk management has become a new breakthrough in the field. With the traditional method compared to the correlation measure, Copula theory has many advantages. First, the edge of the distribution is not limited restrictions Copula theory can be constructed by the flexible multivariate distribution. Second, Copula Theory in the build financial models, the marginal distribution of random variables can be divided further study of related structures, including related structures by a Copula function to describe, this modeling structure is simplified, and the analysis of financial activities Understanding can also be a great benefit.VaR mostly used to measure portfolio risk, in the VaR estimation, a major difficulty is to simulate the relevant structures, especially in the calculation and distribution of tail-related var. The proposed model is based on a volatility, copula theory and extreme value theory of dynamic economic models. ARMA-GARCH model is fitted with a return value is reasonable to explain the volatility of income levels and conditions. Variance of the observed values are modified to simulate the copula, the tail of the empirical distribution of the marginal distribution or GPD, the other to fit the empirical distribution. Losses associated with larger values observed in the larger weight given to this estimator is used to estimate the copulas. Our main contribution is to propose the marginal distribution and copula estimation process, a process that allows simulation of non-symmetry-related data, but is symmetric copula family related.This paper presents a theory based on extreme value copula and securities VaR estimation. Each simulation yields a joint distribution of copula ARMA-GARCH models to fit the marginal distribution fitted by the GPD and empirical distribution is estimated to give a larger amount of copula estimation weight loss, application of a two-stage application of this method is valuable Securities, compared with traditional methods.

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CLC: > Economic > Fiscal, monetary > Finance, banking > Finance, banking theory > Financial market
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