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研究生： 林君瀌
Jun-Biao Lin
論文名稱： 多資產美式選擇權之評價及其應用
The Algorithms for Valuing American Style Multivariate Contingent Claims: Applications for ESO and other Derivatives
指導教授： 張傳章
Chuang-Chang Chang
口試委員:
學位類別： 博士
Doctor
系所名稱： 管理學院 - 財務金融學系
Department of Finance
畢業學年度： 95
語文別： 英文
論文頁數： 87
中文關鍵詞： 美式選擇權 、多資產
外文關鍵詞： transformed-trinomial approaches, ESO, an extended Markov Chain approach, Weather Derivatives
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    • 傳統上，當標的資產為一特殊分配時，將增加衍生性商品的訂價困難度。Camara 和 Chung (2006) 所提出的轉換的二元樹模型 (Transformed Binomial Tree) 解決了部份難題。然而其模型對處理多資產標的商品仍有不足。因此，本研究提出三種方法，嘗試在轉換為常態架構 (Transformed Normal Method) 下，對多資產標的商品訂價。結果發現，在單一商品下，馬可夫鏈(Markov Chain Model)可得到相對於轉換的三元樹模型 (Transformed Trinomial Tree) 較佳的結果。而當延申到多資產時，Sobol序列馬可夫鏈 (Sobol Sequence Markov Chain Model) 無論在長天期或短天期的衍生性金融商品，皆可獲得最佳的結果。此外，本研究亦將此方法應用至目前熱門的二種商品：員工認股權證(Executive Stock Option) 和氣候選擇權 (Weather Derivatives)。以增加本研究之廣度。

    This dissertation develops three numerical algorithms for pricing European and American multivariate contingent claims. One approach is a multivariate transformed trinomial model. This model is an extension of the Camara and Chung (2006) transformed-binomial model with one underlying asset and a discrete-time version of Schoder (2004) model for pricing European-style options. However, unlike Schoder’s model, our model can easily handle American-style multivariate contingent claims. Another one is the Markov Chain approach provided by Duan and Simonato’s (2001). The other approach is an extended Markov Chain approach which takes Sobol sequences into Duan and Simonato’s (2001) Markov Chain model to accelerate convergence speed. We use numerical examples to show how to use these three methods to value various types of multivariate contingent claims, such as digital options and Executive Stock Option (ESO) and Weather Derivatives.

    Abstract ……………………………………………………………………….…….Ⅰ Contents……………………………………………………………………………..Ⅳ List of Figures………………………………………………………………………Ⅶ List of Tables………………………………………………………………………..Ⅷ 1 Introduction……………………………………………………………………..1 1.1 Motivation…………………………………………………………………..1 1.2 Objectives…………………………………………………………………..2 2 Literature Review………………………………………………………………4 2.1 Methodology………………………………………………………………..4 2.2 Executive Stock Options……………………………………………………5 2.3 Weather Derivatives………………………………………………………...7 3 Methodology 3.1 One Underlying Asset………………………………………………………9 3.1.1 The Transformed-Trinomial Model…………………………………9 3.1.2 The Markov Chain Model…………………………………………15 3.2 Models for Pricing options with Multiple Underlying Assets……………..18 3.2.1 The Transformed-Trinomial Model………………………………..18 3.2.2 The Standard Markov Chain Method……………………………...22 3.2.3 The Sobol Markov Chain Method…………………………………22 4 Numerical Examples and Convergence………………………………………27 4.1 The Case of Option with one Underlying Asset…………………………...27 4.2 The Case of Option with two Underlying Assets………………………….29 5 Executive Stock Options…………………………..…………………………..40 5.1 Introduction……………………………………….……………………….40 5.2 Economic Settings…………………………………………..…………….41 5.3 Numerical Results…………………………………………………………44 6 Weather Derivatives…………………………………………………………..59 6.1 Introduction………………………………………………………………..59 6.2 Economic Settings…………………………………………………………61 6.3 Numerical Results…………………………………………………………64 7 Concluding Remarks and Future Research………………………………….70 Reference…………………………………………………………………………….72

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