| Variance as a risk measure is subject to a lot of criticism. First, Variance can not characterize the risk of non-symmetry. Second, for some distribution of specific risks (such as credit risk), the second-order moments may not exist. Since J.P. Morgan made the RiskMetric public in1994, which was based on VaR model, VaR has become the industry standard risk measure in financial industry. Let X represent the profit or loss of random variables, F denote a function of the marginal distribution of X, the mathematical definition of VaR can be as follows:VaRa (x)=inf (x∈R, F (x)> a)VaR has widely used in practice, but in theory there are some flaws. It is well-known that VaR is not a coherent risk measure which does not satisfy the subadditivity axiomatic condition. However, VaR is defined as the maximum possible loss of hold portfolio with in specific time on a certain confidence level, which is understood by regulators, management and market participants easily, and Danielesson et al.(2005) think although there are many criticisms on VaR, which are not very important in practice. Now, there are more than1000banks, non-financial institutions, mutual fund, insurance companies and other asset management institutions claim to use VaR to measure the risk of financial Market.But VaR theory is not perfect. There are many questions on VaR theory and practice in different aspects as followed:Firstly, how to accurate fit the asymmetry and fat-tailness characteristics of P&L distribution determine the effectiveness of the VaR model; Second, different VaR estimation method can get different VaR value, there still haven’t been a simple and precise VaR method until now; Thirdly, how to build VaR evaluation system is the key to financial risk management based on VaR method, But there still haven’t been a standard VaR evaluation system until now. Finally, for non-elliptical distribution, VaR does not fatisfy the additive condition, which is not a coherent risk measure, so how to improve the VaR model and to seek alternative method is a research hotspot currently.By concluding the current literature, this article study both VaR estimation and VaR backtesting. There are three estimation methods, which are parametric methods (such as GARCH method, RiskMetric), semi-parametric methods (such as extreme value theory, CAViaR) and non-parametric methods (such as historical simulation method). Although semi-parametric method and non-parametric method have the advantage that impose fewer constraints and assumptions on the true data generating process, these two method can estimate the gradual covariance matrix of VaR difficultly. The parametric method imposes some strong constraints, but this method can be estimated and tested easily. However, the forecasting quality of VaR model estimated by parametric method is decided to the correct assumption on P&L distribution. Empirical studies have shown that the tail of the distribution of financial assets yield is not like normal distribution as rendering index squared attenuation, which is thicker than normal distribution. Another important feature of P&L distribution is asymmetry, which is also called leverage effect, this is because investors are generally more concerned about the downside risk. Komunjer(2007) think that distribution family selected must be able to contain the most common benchmark distribution:such as normal distribution and Laplace distribution, and be able to simulate the various features of the real market data:fat-tailness and asymmetry, which also has closed density function form in order to facilitate estimation and testing. Stable distribution, Person distribution family, Tukey-μ distribution family can fit a wide range of skewness and kurtosis and describe the two feather of P&L distribution well, but these distributions does not have a closed density function form which cannot be estimated by maximum likelihood estimation method. Skewed T distribution can also be used to fit these two feathers of P&L distribution, which is the expansion of T distribution and has been used in financial risk management widely. But this distribution has some defects:the density function of skewed T distribution is not log-concave and there may be no finite fourth-order moment while the degree of freedom is less than4. Gram-Charlier distribution can also use to simulate the P&L distribution, but we must impose some constraints on the skewness and kurtosis which can meet the condition that density function is non-negative, furthermore the maximum likelihood estimation of parameters are significantly influenced by the initial value. So, this article use Komunjer’s APD to fit the P&L distribution and build VaR model based on APD distribution. We use statistics and finance research tools, combined with quantitative empirical method and qualitative analysis, and focus on the theory and practice of financial risk measure based on APD-VaR method. We study the statistic characteristics of APD distribution, and propose a dynamic VaR method:GARCH-APD-VaR.As we know, there are many methods can estimate VaR, which means that means that we can get different risk assessment for the same asset and portfolio, even very large differences. Therefore, we should verify the VaR model, there have been many backtesting methods in literature, this article discusses the so-called "event probability prediction method". In this method, we check the process that the real return series breakthrough the VaR forecast sequence, which contains two parts:the non-conditional coverage teat and independence test. Currently, the mainstream method in application level is likelihood ratio test, which assumes that the data meet the first-order Markov chain. In actual use the data may not satisfy this assumption, furthermore this test does not consider the existence of high-order autocorrelation and other exogenous variables which can also affect the effectiveness of the VaR model. Based on this, we consider a newer VaR model validation method:dynamic quantile test, as a supplement for likelihood ratio test, we establish a VaR evaluation system combined with likelihood ratio test and dynamic quantile test.The main research work and achievements can be summarized as follows:1.In introduction part of this article, we described the research background and indicate the study direction, propose the question this article should solve.2. In second part, we also summarize the literatures, discuss the origin, development of VaR method in depth, analysis the scope and limitations of VaR estimation methods and VaR backtesting methods.3. The main work of this part is study the theory and methods of financial risk management, we elaborated the concept, characteristics and classification of financial risks, we gave a detailed analysis of the motives, function and management of financial risk measures, and discussed the risk measures with their historical evolution and financial risk measurement framework.4. In this part, we focused on the principles, definitions and estimation methods of VaR, we introduced GARCH process to achieve dynamic VaR model, on this basis we propose the GARCH-APD-VaR method.5. In chapter five,the author introduced many VaR backtesting methods, and analysised the assumptions, characteristics and limitations of each method.6. In empirical analysis, we chose SSCE gain data as risk factor, we note that there are fat-tailness and asymmetry phenomenon in return series with first-order autocorrelation and second-order autocorrelation, which indicates that the introduction of GARCH and APD is reasonableness. In this part, we chose normal distribution, the generalized power distribution and skewed T distribution as competitor for the asymmetric power distribution. Based on likelihood ratio test, we found that APD-VaR model is the optimal model on both95%confidence level and99%confidence level. However, if we chose the DQ test, we found that the results is very different from LR test, on95%confidence level there are a small amount of models qualified, but on99%confidence level there is no model qualified. This is surprise! Because we cannot observe the true value of VaR, these results make us to focus on the important of VaR model evaluation.7. This part is conclusion of this article, we summarize the study and make a outlook on future research.The innovations of this article as follows:proposed the dynamic VaR method based on APD distribution; proposed a VaR backtesting system which combined with LR test and DQ test. The author attempts to provide some valuable information for both VaR estimation and VaR backtesting. |
PDF Full Text Request