臺灣博碩士論文加值系統

在這篇論文中，我們用廣義極端分配來衡量風險。由於在金融市場中，報酬率的分配往往是未知的，我們可以根據極端值定理，將焦點放在未知分配F的尾端，這些尾端值通過適當的轉換後，會收斂至三種可能的分配裡的其中一種。以區間最大法而言，這三種分配可以統一用廣義極端值分配概括表示；另一種常用的方法是過峰值法，其會收斂至廣義帕利托分配。雖然區間最大法比過峰值法早提出，卻因為過峰值法能夠保留分配尾端較多資訊，所以較受理論研究的青睞，然而，區間最大法已經被證明擁有良好的統計性質[Ferreir and de Haan (2015)]。Dombry (2013)也證明了其最大概似估計量的一致性。在報酬率經由AR(1)-GARCH(1,1)模型過濾後，比較兩種方法在計算不同金融商品風險值上的效果，如巴塞爾銀行監督委員會(Basel Committee on Banking Supervision)於1996年建議金融機構採用回饋測試來檢測風險值估計模型的準確性，我們亦對多項金融商品進行回測，然後對估計而得的風險值以Christoffersen (1998)提出的條件涵蓋率檢定其準確度。

In this paper issue of tail risk can be estimated using the generalized extreme value (GEV) distribution. In financial market the distribution of returns are hard to find. By extreme value theory (EVT), we should focus on the tail of the distribution F, which can converge to one of three possible distributions. The three distributions of block maxima can be written in a unified manner by means of the GEV distribution. The alternative approach widely used is the peaks over threshold method, which has generalized Pareto distribution (GPD). Though the block maxima is proposed earlier than the peaks over threshold method, much theoretical research has gone into the peaks over threshold method because it can retain more information in the tail of the distribution. However the block maxima method estimators has been proved its fine statistical properties [Ferreir and de Haan (2015)]. Dombry (2013) proved consistency of the maximum likelihood estimators. The present paper provides a comparative study of both methods to estimate VaR with returns filtered by AR(1)-GARCH(1,1) model. As Basel Committee on Banking Supervision proposed financial institute to backtest the accuracy of VaR estimation in 1996, we conduct backtest on various financial products and test the accuracy of VaR estimation using Conditional Coverage Test proposed by Christoffersen(1998).

Chinese Abstract i
English Abstract ii
Acknowledgement iii
Table of Contents iv
List of Tables v
List of Figures vi
1. Introduction 1
2. Literature Review 3
3. Methods 5
3.1 Definition of VaR and ES estimation 6
3.2 EVT approach to VaR and ES estimates 7
3.3 Data 14
4. Estimation Result 15
5. Concluding Remarks 23
References 24

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