Importance sampling for Value-at-Risk computations under factor model

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呂駿杰(Chun-Chieh Lu) 查詢紙本館藏

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統計研究所

論文名稱

(Importance sampling for Value-at-Risk computations under factor model)

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摘要(中)

風險價值(VaR)，它被定義為一個給定的時間範圍內利潤和
損失分佈的條件分位數。雖然蒙地卡羅模擬是評估投資組合
風險價值最有效的方法，這種方法主要的缺點在於需要大量的
計算需求。所以在本文中，我們考慮在因子模型之下的重要性
採樣。此外，我們對風險因子建模在多元常態分配和多元t分
配。在此假設之下，引用upper bound 和optimal tilting 兩
種方法來尋找新測度的最佳解。最後，比較重要性採樣和蒙地
卡羅的相對效率。我們可以看出重要性採樣顯著地比蒙地卡羅
來的更好。

摘要(英)

Value-at-Risk (VaR), which is defined as the conditional quantile of the profit-and-loss distribution for a given time horizon. Although the Monte Carlo simulation is the most powerful method to evaluate portfolio VaR, a major drawback of this method is that it is computationally demanding. So in this paper, we consider the efficient importance sampling method under factor model. Furthermore, we model the risk factors with multivariate normal
distribution and multivariate t distribution. Among this assumptions, we introduce upper bound method and optimal tilting method to find the alternative measure Q. In the end, we give the relative efficiency of importance sampling method and Monte Carlo method. We show that the importance sampling method is significantly better than Monte Carlo method.

關鍵字(中)

★ 重要性採樣
★ 因子模型
★ 投資組合風險值
★ 多元分布

關鍵字(英)

★ Importance sampling
★ factor model
★ portfolio VaR
★ multivariate distribution

論文目次

Abstract I
Table of Contents III
List of Figures V
List of Tables VI
Chapter 1 Introduction 1
Chapter 2 Preliminaries 4
2.1 Risk measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Factor model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Dynamic factor model . . . . . . . . . . . . . . . . . . . . . . . 6
Chapter 3 Importance sampling method 9
3.1 FM-IS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 DFM-IS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 The multivariate normal distribution case . . . . . . . . 16
3.2.2 The multivariate t distribution case . . . . . . . . . . . . 19
Chapter 4 Simulation study 31
4.1 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 FM-IS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.3 DFM-IS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3.1 The multivariate normal distribution case . . . . . . . . 37
4.3.2 The multivariate t distribution case . . . . . . . . . . . . 40
Chapter 5 An Application 44
Chapter 6 Conclusion 49
Reference 50

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指導教授

傅承德(Cheng-Der Fuh)

審核日期

2016-6-29

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