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研究生： 蔡明軒
Tsai, Ming-Hsuan
論文名稱： 波動非對稱下之跳躍擴散模型與風險值應用
Jump Diffusion Model with Asymmetry of Volatility for VaR
指導教授： 黃銘欽
Huang, Min-Ching
學位類別： 碩士
Master
系所名稱： 管理學院 - 統計學系
Department of Statistics
論文出版年： 2013
畢業學年度： 101
語文別： 英文
論文頁數： 30
中文關鍵詞： 風險值 、跳躍擴散模型 、波動不對稱GARCH模型
外文關鍵詞： VaR, Jump Diffusion Model, Asymmetric Volatility GARCH Model
相關次數： 點閱：138  下載：1 
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    • 金融資產報酬率具有高狹峰與偏態等特性，傳統的常態分配假設下之資產報酬率模型無法描述此現象；更甚者，資產報酬率常受到外在因素影響，導致資產價格呈現瞬間跳躍，跳躍擴散模型因此蓬勃發展。本研究修改Kou(Kou, 2002)之跳躍振幅為非對稱雙指數分配模型，並結合GJR-GARCH 模型，其結果與Kou(Kou, 2002)及Hanson和Westman(Hanson & Westman, 2002)之跳躍模型進行比較。實證結果顯示:應用在台灣加權指數方面，本研究所提出之模型得到較準確風險值評估。

    Financial asset returns have some characteristics of leptokurticity and skewness. Traditional normality assumption of the return distribution couldn’t describe this phenomenon. What’s more, financial asset returns are often affected by external factors which lead to instant price jumps. Jump diffusion models therefore attract more and more attention. This thesis modifies the asymmetric double-exponential jump-amplitude model proposed by Kou(Kou, 2002) and combines it with the GJR-GARCH volatility model. The result of this research is compared with the Kou (Kou, 2002) and Hanson & Westman (Hanson & Westman, 2002) jump models. Our empirical study on TAIEX index data shows the proposed model gives more accurate VaR.

    Table of Contents 摘要 I Abstract II 致謝 III Table of Contents IV Tables V Figures V Chapter 1 Introduction 1 1-1 Research Background and Motivation 1 1-2 Purpose of Research and Frameworks 2 Chapter 2 Literature Review 3 2-1 Value at Risk 3 2-2 Volatility Model 6 2-2-1 SMA and EWMA 7 2-2-2 GARCH Models 7 2-3 Back-Testing 8 2-3-1 Frequency of Losses 9 2-3-2 Root Mean Square Error (RMSE) 9 Chapter 3 Methodology 11 3-1 Jump Diffusion Stochastic Process 11 3-1-1 Diffusion Stochastic Process 12 3-1-2 Jump Diffusion Stochastic Process 12 3-2 Proposed model 14 3-2-1 Jump Amplitude 14 3-2-2 Parameter Estimation 17 3-2-3 Proposed Model with GJR-GARCH Volatility 18 Chapter 4 Empirical study 20 Chapter 5 Conclusion 25 References 26 Appendix 28

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