A Study On Tail Risk Of Portfolio Under Asymmetric Laplace Distribution

In recent years, the frequent occurrence of extreme financial events, people are increasingly pay attention to tail risk management. For a long time, the popular tail risk measure models include value-at-risk(VaR), tail conditional expectations(TCE)and conditional value-at-risk(CVaR). These models can measure the expectation of tail loss beyond VaR, but not measure the tail variability along the tail loss. As a new risk measure, the tail conditional variance(TCV) can reflect the variability of the tail loss. Therefore, it is more reasonable that VaR, TCE and TCV are synthesized with the measurement of tail risk. There are numerous empirical studies show that the distribution of asset returns not only present the feature of peak, fat-tails and skewness, but also has an asymmetric distribution. Therefore, in this thesis, we study the value-atrisk, tail conditional expectation and tail conditional variance under the hypothesis of an asymmetric Laplace distribution. We derive the explicit expressions of all these tail risk measures and analyze the parametric sensitivity of the tail risk. Finally, we give an empirical analysis of the Chinese stock market. The empirical results show that the parametric estimation of the tail risk is close to the sample estimation under the assumption of asymmetric Laplace distribution. Therefore, the asymmetric Laplace distribution can be applied to model accurately tail risk. The empirical results also show the distribution of the asset returns has a thicker right tail.