# 臺灣博碩士論文加值系統

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 本研究修正Ritchken and Trevor (1999) 提出的GARCH選擇權樹狀訂價法與Duan, Popova and Ritchken (2002) 提出的Markov-switching 選擇權樹狀訂價法的缺失，以此為基礎，進一步提出更具一般化的Markov-switching GARCH (簡稱MS-GARCH)選擇權樹狀訂價法，以解決標的資產價格動態過程服從MS- GARCH過程下之歐式與美式選擇權評價問題。由於GARCH模型與Markov-switching模型皆可視為MS-GARCH模型的特例，故本文所提之MS-GARCH選擇權樹狀訂價法相當具有一般性。數值分析結果顯示，既有的GARCH選擇權樹狀訂價法與Markov-switching選擇權樹狀訂價法在考慮本文所提出的修正與補強之後，計算上比既有的方法簡單，準確度也較高。除此之外，數值分析結果亦顯示MS-GARCH選擇權樹狀訂價法具有相當良好的收斂性與正確性。
 This paper supplements the GARCH lattice algorithm for option pricing developed by Ritchken and Trevor (1999) and proposes possible modifications for Markov-switching lattice algorithm of Duan, Popova and Ritchken (2002), respectively. The numerical analyses show that our modifications for these existent lattice algorithms result in either less complicated procedures or faster rates of convergence. On the other hand, the Markov-switching GARCH models (MS-GARCH) which combine GARCH models with Markov-switching processes are highly flexibility and widely used in financial time-series analysis. Accordingly, this study further develops a new efficient lattice algorithm to price European and American options under discrete time MS-GARCH processes. The new option pricing model considered assumes that the underlying stock price dynamic is modeled by the process in which prices remain in one GARCH process for a random amount of time before switching over into another GARCH process. Since both of GARCH option models and Markov-switching option models are special cases of the MS-GARCH models, the new lattice algorithm is very general. We also conduct numerical analyses to gauge the convergence and accuracy of option prices produced by the lattice to their true values. These results are very satisfactory.
 Table of Contents1. Introduction 12. Literature review 33. The GARCH option model 6 3.1 The lattice algorithm for the GARCH option model 6 3.2 Possible modifications for the GARCH lattice 12 3.3 Numerical analyses of our modification 164. The Markov-switching option model 18 4.1 The lattice algorithm for the Markov-switching option model 19 4.2 Possible modifications for the Markov-switching lattice 22 4.3 Numerical analyses of our modification 245. The MS-GARCH model 26 5.1 The lattice algorithm for the MS-GARCH option model 29 5.2 Numerical analyses of MS-GARCH lattice algorithm 366. Conclusion 39References 40
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 1 An Efficient GARCH Numerical Option Pricing Model

 1 18.游彌堅。〈談兒童讀物—介紹愛兒文庫和東方少年文庫〉，臺北市：《臺灣教育》月刊第31期。頁1。1953年7月1日。 2 17.邱各容。〈從意識型態談日治時期臺灣兒童文學發展研究〉，臺北市︰《全國新書資訊月刊》第100期。頁25-31。2007年4月。 3 15.邱各容。〈日治時期臺灣兒童文學勾微〉，臺北市︰《全國新書資訊月刊》第60期。頁22-32。2004年1月。

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