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博碩士論文 etd-0728114-212246 詳細資訊
Title page for etd-0728114-212246
論文名稱
Title
運用關連結構模型及重點抽樣法估計投資組合的期望損失
Importance sampling estimation of portfolio expected shortfall via copula approach
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
31
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2014-07-24
繳交日期
Date of Submission
2014-08-28
關鍵字
Keywords
關聯結構、核密度估計、期望損失、重點抽樣法、C藤、D藤
D-vine, copula, kernel density estimation, expected shortfall, importance sampling, C-vine
統計
Statistics
本論文已被瀏覽 5749 次,被下載 46
The thesis/dissertation has been browsed 5749 times, has been downloaded 46 times.
中文摘要
期望損失是一個評估財務投資組合風險的測度。本篇研究討論一個投資組合期望損失的估計問題。首先我們使用二維的關聯結構來描述雙變量間的相關性結構,並利用C藤或D藤關聯結構的方式來建構投資組合多維資產的聯合分布。我們從配適的關聯結構模型的聯合分布中,應用拔靴法抽樣,並且使用核密度法來估計投資組合損失的密度。我們進一步使用回歸的方法改善分布尾端的估計,並使用重點抽樣法改進估計期望損失的效率。
Abstract
Expected shortfall is a measure of financial portfolio risk. In this study, we consider the problem of estimating expected shortfall of a portfolio. We use bivariate copula to describe the dependence between two variables. And construct joint density for the assets of the portfolio using C-vine or D-vine approach based on pair-copulas. We draw bootstrap samples from the fitted copula-based joint distribution and estimate the density of the portfolio loss by kernel method. Regression method is further used to smooth the kernel estimator for the tail part of the density function. To improve estimation efficiency of the expected shortfall, we use the importance sampling estimate based on exponential truncation approach.
目次 Table of Contents
論文審定書 i
致謝 ii
摘要 iii
Abstract iv
1 Introduction 1
2 Vine copulas 2
2.1 Copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Pair-copula constructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 C-vine, D-vine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Density estimation of the portfolio loss 7
3.1 Kernel density estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Smoothing method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4 Estimation of ES 8
5 Simulation study 10
5.1 Simulation under 2-dim setting . . . . . . . . . . . . . . . . . . . . . . . . 10
5.2 Simulation under high-dim setting . . . . . . . . . . . . . . . . . . . . . . . 11
6 Real example 12
7 Discussions and conclusions 14
References 15
A Appendix 17
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