Study On Value At Risk Based On Asymmetric Laplace Distribution

VaR (Value at Risk for short VaR) is a common measure of market risk tools, and can be seen as the cornerstone of market risk measurement. VaR has succeeded in creating a broad-based consensus,emerging as a concise and relevant method for gauging the level of market risk incurred by financial institutions. Now VaR model has gained extensive use by financial and regulatory communities.In the VaR calculation, the distribution of sequences for the financial data is essential. Parametric methods assume that rate of return subjects to a certain degree of distributions, and the calculation of the process often requires an estimate of the value of the parameter. But the result is depended on the correct assumption. When the assumption is incorrect, the parameters may have a greater error. The assumption is a relatively large number of Normal Distribution, mixed Normal Distribution, t Distribution and Laplace Distribution, but they are only described the distribution of fat-tail nature of the sequences, not shown bias defect. Asymmetric Laplace Distribution is leptokurtic, thick-tail and skew, not only considers the fat-tail problem, but also takes the financial characteristics of skewness into account, so the introduction of Asymmetric Laplace Distribution is to study on VaR. Research papers ideas and contents are as followed:①Based on the analysis of the status quo at home and abroad for VaR methodology study, this thesis systematically studies and contrasts the distribution of financial data series, compares the distribution of current applications in the advantages and disadvantages of VaR, studies and extends symmetric Laplace distribution, so make it can have a non-symmetry to reflect the skewness characteristic of financial data sequences.②For positive and negative rate of return, they have been given different weights. To the location parameter of Laplace distribution for reference, by virtue of indicative function thesis introduces non-symmetric Laplace distribution, analyzes and researches the property of non-symmetric Laplace distribution and parameter's maximum likelihood estimation, and studies the corresponding VaR calculation.③Some empirical examples given in this thesis demonstrate that Asymmetric Laplace Distribution with steep peak, heavy tail and skewness possesses important applied value in financial field. The structure of the paper is as followed. Chapter 1 is introduction. Chapter 2 recalls the origination and notion of VaR as well as its main models: parametric method, historical simulation, Monte Carlo simulation and extreme value theory. Chapter 3 introduces Asymmetric Laplace Distribution as well as its main properties and parameter estimations and the calculation of VaR. Chapter 4 demonstrates the application value and practical significance of the Non-symmetrical Laplace Distribution by expatiating a number of empirical applications. The last chapter summarizes and concludes.