在雙指數跳躍擴散過程下動態保本型商品之評價分析

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研究生：	連雅慧 Ya-Huei Lian
論文名稱：	在雙指數跳躍擴散過程下動態保本型商品之評價分析 Pricing Dyanmic Guaranteed Funds Under a Double Exponential Jump Diffusion Process
指導教授：	張傳章 Chung-Chang Chang
口試委員:
學位類別：	碩士 Master
系所名稱：	管理學院 - 財務金融學系 Department of Finance
畢業學年度：	97
語文別：	英文
論文頁數：	41
中文關鍵詞：	動態保本型基金、跳躍擴散、拉普拉斯轉換
外文關鍵詞：	Dynamic Guaranteed Funds, Jump Diffusion, Laplace Transform
相關次數：	點閱：15 下載：0
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本篇論文拓展過去文獻對於動態保本型基金之評價分析。本文假設標的基金價格服從雙重指數跳躍擴散的過程，並在此假設下對於動態保本型基金進行評價分析。首先，本文給出動態保本型基金價格拉普拉斯轉換之封閉解，並進一步應用Gaver-Stehfest 演算法進行拉普拉斯逆轉換，求得動態保本型基金的價格。從文章中之數值結果可以發現本文所提出之評價方法相較於蒙地卡羅模擬更具有效率性而且不失準確性。另一方面，本文亦研究在考慮價格跳躍的情況下，動態保本型基金之價格改變行為。最後，本篇論文亦提供動態保本型基金價格與相關模型參數之敏感性分析。

This paper complements the extant literature to evaluate the prices of dynamic guaranteed funds when the price of underlying naked fund follows a double exponential jump-diffusion process. We first derive the closed-form solution for the Laplace transform of dynamic guaranteed fund price, and then apply the efficient Gaver-Stehfest algorithm of Laplace inversion to obtain the prices of dynamic guaranteed funds. Based on the numerical pricing results, we find that the proposed pricing method is much more efficient than the Monte Carlo simulation approach although it loses a sufficiently small accuracy. On the other hand, we also provide an investigation on the behavior of prices of dynamic guaranteed funds when jumps are taken into consideration. In addition, the sensitivity analyses of the prices of dynamic guaranteed funds with respect to jump-related parameters are also given in this paper.
Key

Content
中文摘要 ······························································································· i
Abstract ································································································· ii
誌謝 ····································································································· iii
Content ·································································································· iv
List of Tables ··························································································· v
List of Figures ·························································································· v
1. INTRODUCTION ················································································ 1
2. THE DOUBLE EXPONENTIAL JUMP-DIFFUSION MODEL ························· 5
2.1. The Model ···················································································· 5
2.2. Distribution of The First Passage Times ················································· 7
3. THE VALUATION OF DYNAMIC GUARANTEED FUNDS ·························· 9
4. NUMERICAL RESULTS ······································································ 12
4.1. Analytical Valuation and Simulation of Dynamic Guaranteed Funds ·············· 12
4.2. Sensitivity Analysis ······································································· 15
5. CONCLUSION ·················································································· 16
REFERENCES ······················································································· 17
APPENDIXES ························································································ 19
Appendix A ······················································································ 19
Appendix B ······················································································ 20
Appendix C ······················································································ 21
Appendix D ······················································································ 22
v
List of Tables
Table 1 ································································································· 23
Panel A ···························································································· 23
Panel B ···························································································· 24
Panel C ···························································································· 25
Table 2 ································································································· 26
Panel A ···························································································· 26
Panel B ···························································································· 28
Panel C ···························································································· 30
Table 3 ································································································· 32
Panel A ···························································································· 32
Panel B ···························································································· 34
Panel C ···························································································· 36
Table 4 ································································································· 38
List of Figures
Figure 1 ································································································· 9
Figure 2 ································································································ 39
Figure 3 ································································································ 40
Figure 4 ································································································ 41

                                

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