Importance sampling for VaR and ES calculations under GARCH model

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許致榕(Chih-Jung Hsu) 查詢紙本館藏

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統計研究所

論文名稱

(Importance sampling for VaR and ES calculations under GARCH model)

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摘要(中)

風險價值（VaR）不只廣泛應用在投資組合的風險測量上，也成為風險管理的重要基準；條件風險值（ES）也是風險測度指標而且包含更多關於分布尾端的資訊。因此，VaR和ES的評估精確度受到越來越多的關注。在此篇論文，我們使用一個對稱的GARCH（1,1）模型。然後，我們採用一個方法－importance sampling technique，來減少變異數且精確地估計VaR與ES。此外，importance sampling technique可以得到與其他的方法一樣的精確度但卻使用較少的樣本。在最後，我們展示我們的方法importance sampling technique優於其他方法。

摘要(英)

Value-at-risk (VaR) is not only broadly used in portfolio risk measurement but also becomes an important benchmark in risk-management. Moreover, expected shortfall (ES) is a risk measure and has more information about the distribution of returns in the tail. Thus, evaluating precision of VaR and ES is getting more attention. In this paper, we suggest a symmetric GARCH(1,1) model to fit the loss data. Then, we propose an importance sampling technique to reduce the variance and estimate VaR and ES accurately. Besides, we find the method with importance sampling which can get the same precision like other methods but using less sample sizes. In the end, we show the method with importance sampling technique outperforms other methods.

關鍵字(中)

★ 風險價值
★ 條件風險值
★ 厚尾
★ GARCH模型

關鍵字(英)

★ Value-at-risk
★ Expected shortfall
★ Heavy tailed
★ GARCH model

論文目次

Contents
摘要 i
Abstract ii
致謝 iii
List of Figures vi
List of Tables vii
1 Introduction 1
2 Preliminaries 3
2.1 Model 3
2.2 Risk measure 4
3 Estimation methods 6
3.1 Historical simulation 6
3.2 Normal and T conditional distribution 7
3.3 The Hill estimator 8
3.4 Filtered historical simulation 9
3.5 Importance sampling 10
3.3.2 The normal distribution case 10
3.3.2 The t-distribution case 15
4 Numerical results 22
4.1 The normal case 22
4.2 The t-distribution case 24
4.3 Empirical Study 29
5 Conclusion 31
Reference 33

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指導教授

傅承德

審核日期

2013-7-2

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