請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/91219完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 呂育道 | zh_TW |
| dc.contributor.advisor | Yuh-Dauh Lyuu | en |
| dc.contributor.author | 胡祖望 | zh_TW |
| dc.contributor.author | TSU-WANG HU | en |
| dc.date.accessioned | 2023-12-12T16:16:09Z | - |
| dc.date.available | 2023-12-13 | - |
| dc.date.copyright | 2023-12-12 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-11-13 | - |
| dc.identifier.citation | Peter Carr and Dilip Madan. Option valuation using the fast Fourier transform. Journal of Computational Finance, 2(4):61–73, 1999.
Pavel Čížek, Wolfgang Härdle, Rafał Weron, and Wolfgang Härdle. Statistical tools for finance and insurance. Berlin: Springer, 2011. Jim Gatheral. Jump-diffusion models. Encyclopedia of Quantitative Finance, 2010. Steve G Kou. Jump-diffusion models for asset pricing in financial engineering. Handbooks in Operations Research and Management Science, 15:73–116, 2007. Steven G Kou and Hui Wang. Option pricing under a double exponential jump diffusion model. Management Science, 2004. Kazuhisa Matsuda. Introduction to Merton jump-diffusion model. Department of Economics, The Graduate Center, City University of New York, New York City, 2004. Nicolas Privault. Stochastic finance: An introduction with market examples. New York City: CRC Press, 2013. Martin Schmelzle. Option pricing formulae using Fourier transform: Theory and 45 application. https://pfadintegral.com/docs/Schmelzle2010%20Fourier%20Pricing.pdf, 2010. Peter Tankov and Ekaterina Voltchkova. Jump-diffusion models: A practitioner’s guide. Banque et Marchés, 99(1):24, 2009. Matthias Thul and Ally Zhang. Analytical option pricing under an asymmetrically displaced double gamma jump-diffusion model. Swiss Finance Institute Research Paper Series 17-78, Swiss Finance Institute, December 2017. Jari Toivanen. Numerical valuation of European and American options under Kou’s jump-diffusion model. SIAM Journal on Scientific Computing, 30(4):1949–1970, 2008. Wikipedia contributors. Gamma distribution — Wikipedia, the free encyclopedia. https://en.wikipedia.org/w/index.php?title=Gamma_distribution&oldid=1165564801, 2023. Wikipedia contributors. Wald’s equation — Wikipedia, the free encyclopedia. https://en.wikipedia.org/w/index.php?title=Wald%27s_equation&oldid=1152633682,2023. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/91219 | - |
| dc.description.abstract | 本論文主要在研究在將Kou 的雙指數跳躍擴展成雙伽瑪跳躍擴散模型。我們採用快速傅立葉轉換方法來獲取兩個模型的選擇權價格。通過將模型擴展為雙伽瑪分佈不僅能夠再現Kou 模型的結果，還能夠提供更大的靈活性來模擬市場，允許對模型進行微調。數值結果顯示雙伽瑪分佈變數如何影響分配的動差，從而導致選權權價值的變化。 | zh_TW |
| dc.description.abstract | This paper aims to extend Kou’s double exponential jump-diffusion model to the double gamma jump-diffusion model. We employ the Fast Fourier Transform method to obtain option prices for both models. By extending the model to the double gamma distribution not only reproduces the results of Kou’s model but also provides enhanced flexibility in simulating the market, allowing for fine-tuning of the model. The numerical results show how the double gamma distribution variables affect the moments leading to changes in the call value. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-12-12T16:16:09Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-12-12T16:16:09Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii Abstract v 摘要 vii Contents ix List of Figures xi List of Tables xiii Chapter 1 Introduction 1 Chapter 2 Motivation and Literature Review 3 2.1 Literature Review 3 2.1.1 Option pricing models 3 2.1.2 Numerical methods for option pricing 4 2.2 Motivation 5 Chapter 3 Our Proposed Model and Numerical Methods 9 3.1 The jump-diffusion model 9 3.1.1 Stochastic differential equation for the jump-diffusion model 9 3.1.2 Martingale condition of jump-diffusion model 12 3.2 The Fast Fourier Transform (FFT) 14 3.2.1 Methodology 14 3.2.2 The CF of the DGJD model 16 3.3 Moments of the jump-size distribution 18 Chapter 4 Numerical Analysis Results 19 4.1 Sanity test 19 4.2 Influences of the variables on the double gamma distribution 20 4.3 Influences of the DG distribution on call prices 23 4.3.1 Results with fixed moments as variables are varied 23 4.3.2 Results with fixed θ1, θ2 and p but varying ρ1 and ρ2 33 4.3.3 Results with fixed ρ1, ρ2 and p but varying θ1 and θ2 36 4.3.4 Results with fixed θ1, θ2, ρ1 and ρ2 but varying p 38 Chapter 5 Conclusions 41 Chapter 6 Future Works 43 References 45 | - |
| dc.language.iso | en | - |
| dc.subject | 指數分佈 | zh_TW |
| dc.subject | 伽馬分佈 | zh_TW |
| dc.subject | 快速傅立葉轉換 | zh_TW |
| dc.subject | 選擇權定價 | zh_TW |
| dc.subject | 指數分佈 | zh_TW |
| dc.subject | 跳躍擴散模型 | zh_TW |
| dc.subject | 選擇權定價 | zh_TW |
| dc.subject | 快速傅立葉轉換 | zh_TW |
| dc.subject | 伽馬分佈 | zh_TW |
| dc.subject | 跳躍擴散模型 | zh_TW |
| dc.subject | Option value | en |
| dc.subject | Jump-diffusion model | en |
| dc.subject | Exponential distribution | en |
| dc.subject | Gamma distribution | en |
| dc.subject | Fast Fourier Transform | en |
| dc.subject | Option value | en |
| dc.subject | Jump-diffusion model | en |
| dc.subject | Exponential distribution | en |
| dc.subject | Gamma distribution | en |
| dc.subject | Fast Fourier Transform | en |
| dc.title | Kou 的跳躍擴散模型擴展：納入雙伽瑪分佈的跳躍幅度 | zh_TW |
| dc.title | An Extension of Kou's Jump-Diffusion Model to Incorporate Double-Gamma Distributed Jump Sizes | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-1 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.coadvisor | 繆維中 | zh_TW |
| dc.contributor.coadvisor | Wei-Jhong Miao | en |
| dc.contributor.oralexamcommittee | 莊文議;張琬喻 | zh_TW |
| dc.contributor.oralexamcommittee | Wen-I Chuang;Woan-Yuh Jang | en |
| dc.subject.keyword | 跳躍擴散模型,指數分佈,伽馬分佈,快速傅立葉轉換,選擇權定價, | zh_TW |
| dc.subject.keyword | Jump-diffusion model,Exponential distribution,Gamma distribution,Fast Fourier Transform,Option value, | en |
| dc.relation.page | 46 | - |
| dc.identifier.doi | 10.6342/NTU202301443 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2023-11-14 | - |
| dc.contributor.author-college | 管理學院 | - |
| dc.contributor.author-dept | 財務金融學系 | - |
| 顯示於系所單位： | 財務金融學系 | |
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