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研究生: 劉名育
Liu, Ming-yuh
論文名稱: 幾何平均與算數平均重設選擇權的定價
On the pricing of Geometric Average and Arithmetic Average Reset Options
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: 2009
畢業學年度: 97
語文別: 英文
論文頁數: 33
中文關鍵詞: 風險中立Wilkinson近似法監控視窗
外文關鍵詞: risk-neutral valuation, Wilkinson approximation, monitoring window, reset triggers
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  • 平均重設選擇權是一種路徑相依選擇權,其履約價可根據標的資產的平均價格之行為而重新設定。本文研究平均重設買權的定價,重設條款為若標的資產在監控視窗的平均價格小於原始履約價格,則在重設日會將履約價重新設定為此平均價格。我們在風險中立的架構下,推導離散型幾何平均重設選擇權的解析定價公式,當監控視窗內的觀察次數無窮多時,此定價公式變成連續型幾何平均重設選擇權的解析定價公式。我們也利用Wilkinson 近似法推導算術平均重設選擇權的近似訂價公式,模擬結果顯示此近似訂價公式的表現相當準確。

    An average reset option is a path-dependent option whose strike price can be reset according to the behavior of the average price of the underlying asset. This thesis studies the average reset calls whose strike price will be reset to the prevailing average price over the monitoring window if the average price is below the original strike price on the reset date. The discrete geometric average and discrete arithmetic average are considered as the reset triggers. We derive the analytical pricing formula for the discrete geometric average reset call under the risk-neutral valuation. As the observation number goes to infinity, the pricing formula for the continuous geometric average reset call is obtained. For the discrete arithmetic average counterpart, we employ Wilkinson approximation to derive the approximate pricing formula. The simulation result shows that the approximate pricing formula is quite accurate.

    1 Introduction 2 1.1 Background 2 1.2 Motivation 3 1.3 Structure of the Thesis 3 2 Literature Review 4 2.1 Asian Options 4 2.2 Reset Options 5 3 Geometric Average Reset Option 7 3.1 Asset Price Model 7 3.2 Terminal Value 7 3.3 The Price before the Monitoring Window 8 3.4 Some Derivations 9 3.5 Limiting Results (I) 13 3.6 The Price in the Monitoring Window 14 3.7 Limiting Results (II) 16 3.8 Characteristics 17 4 Arithmetic Average Reset Option 21 4.1 Terminal Value 21 4.2 Wilkinson Approximation 22 4.3 Approximate Pricing Formula 22 4.4 Simulation Results 27 5 Conclusion 31 Bibliography 32

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