Evaluating the VaR and Conditional VaR of the Synthesized Data Characteristic of Financial Returns Using the Extreme Value Theory
Date Issued
2014
Date
2014
Author(s)
Tsai, Yong-Xin
Abstract
The global financial crisis in 2008 has raised concerns on the events so called “the Balck Swans”. Evaluating value at risk and conditional value at risk using the extreme value theory can produce the asset loss and the corresponding expected asset loss at certain confidence level under extreme circumstances. This paper uses the synthetic data characteristic of financial returns as research targets, and in this way, we can avoid the drawbacks of analyzing the real market data which are affected by ambiguous variables. There are two types of synthesized data: static data and dynamic data. Static data are asset losses which are randomly sampled from the normal distribution, the Student’s t distribution and the log normal distribution, respectively. Dynamic data are time series generated by using the autoregressive moving average model, the autoregressive conditional heteroscedasticity model. There are two methods to evaluate the value at risk and the conditional value at risk using the extreme value theory: the static method and the dynamic method. The static method includes the block maxima method and the peaks over the threshold. The dynamic method integrates the dynamic model, the peaks over the threshold and the bootstrap sampling to evaluate the risk. For static data, there is no definite relation between statistics calculated from samples, theoretical values and the results calculated by the static method. For the dynamic data, there is a definite relation between the results calculated by the dynamic method, statistics calculated from samples, theoretic values and the results calculated by the dynamic method.
Subjects
極值理論
風險值
條件風險值
區塊最大法
穿越門檻值模型
自我迴歸移動平均模型
非對稱性冪級數自我迴歸條件異質變異數模型
Type
thesis
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