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研究生: 陳建文
Chien-wen Chen
論文名稱: 選擇權資料對EGARCH模型參數估計之影響
The influence of option data on parameter estimate under EGARCH model
指導教授: 傅承德
Cheng-der Fuh
口試委員:
學位類別: 碩士
Master
系所名稱: 理學院 - 統計研究所
Graduate Institute of Statistics
畢業學年度: 97
語文別: 中文
論文頁數: 37
中文關鍵詞: 槓桿效應不對稱效應波動Black-Scholes模型EGARCH模型
外文關鍵詞: Leverage effect, Volatility, Asymmetric effect, Black-Scholes model, EGARCH model
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  • 選擇權在財務金融中儼然已經是一個重要的衍生性商品。一般而言,選擇權與波動率間有著高度的相關性,因此本文在Duan (1995)所提出的GARCH選擇權評價模型建構下,修改成能夠描述不對稱現象的EGARCH模型,使其選擇權評價模型更具彈性。除此之外,擁有更多對母體參數有關的資訊,往往可以增加對參數估計的精確與改良,於是,吾人試圖透過兩種引進選擇權資料的方式,來探討參數估計是否具有更佳的漸進估計結果。然而,從模擬的結果中可以發現,在EGARCH模型中引入選擇權資料,對於參數估計上僅有些許的幫助。


    In the financial finance, options has become an important derivatives. In general, options are highly informative about volatility. Based on the Duan (1995) who proposed the GARCH option pricing model, modified to the EGARCH model which can describe the asymmetry effect, so that the option pricing model will more flexible. In addition, the more information about the population we have, the more precision can be increased on parameter estimation. Therefore, we attempt to introduce options through two ways, and to discuss whether parameter estimation has better asymptotic estimate result. However, the results from the simulation show that introducing the options in the EGARCH model only has a trifle help regarding the parameter estimation.

    中文摘要 ………………………………………………………… i 英文摘要 ………………………………………………………… ii 致謝辭 ………………………………………………………… iii 目錄 ………………………………………………………… iv 圖目錄 ………………………………………………………… v 表目錄 ………………………………………………………… vi 符號說明 ………………………………………………………… vii 第一章 緒論…………………………………………………… 1 1.1 研究背景與動機……………………………………… 1 1.2 研究目的……………………………………………… 6 1.3 論文架構……………………………………………… 7 第二章 文獻回顧……………………………………………… 9 2.1 Black-Scholes模型………………………………… 9 2.2 GARCH家族…………………………………………… 10 2.2.1 ARCH模型…………………………………………… 10 2.2.2 GARCH模型…………………………………………… 12 2.2.3 EGARCH模型…………………………………………… 13 第三章 研究方法……………………………………………… 17 3.1 沒有加誤差項的方式………………………………… 17 3.2 加入誤差項的方式…………………………………… 20 第四章 模擬結果……………………………………………… 22 第五章 結論…………………………………………………… 32 參考文獻 ………………………………………………………… 33

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