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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 呂育道(Yuh-Dauh Lyuu) | |
| dc.contributor.author | En-Tzu Chang | en |
| dc.contributor.author | 張恩慈 | zh_TW |
| dc.date.accessioned | 2022-11-23T09:30:24Z | - |
| dc.date.available | 2023-06-28 | |
| dc.date.available | 2022-11-23T09:30:24Z | - |
| dc.date.copyright | 2021-07-08 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-06-29 | |
| dc.identifier.citation | [1] Mesias Alfeus and Erik Schlögl. On numerical methods for spread options splitting method. In QUANTITATIVE FINANCE RESEARCH CENTRE. 2018. [2] Max Andersson. Valuation of spread options using the fast fourier transform under stochastic volatility and jump diffusion models. In Lund University Faculty of engineering. 2015. [3] Teodora Baeva. On the pricing and sensitivity of spread options on two correlated assets. In SSRN Electronic Journal. 2010. [4] Petter Bjerksund and Gunnar Stensland. Closed form spread option valuation. In Quantitative Finance, volume 14 of 10, page 1785–1794. Norway, 2011. [5] Peter Carr, Morgan Stanley, and Dilip Madan. Option valuation using the fast fourier transform. In Journal of Computational Finance, volume 2. 1999. [6] Kyriakos Chourdakis. Option pricing using the fractional fft. In Journal of Computational Finance, volume 4. 2005. [7] M. A. H. Dempster and S. S. G. Hong. Spread option valuation and the fast fourier transform. In Mathematical Finance—Bachelier Congress, pages 203–220. Springer, Berlin, Heidelberg, 2002. [8] John C. Hull. OPTIONS, FUTURES,AND OTHER DERIVATIVES. Pearson Education, 9th edition, 2015. [9] Thomas Hurd and Zhuowei Zhou. A fourier transform method for spread option pricing. In SIAM Journal on Financial Mathematics, pages 142–157. 2010. [10] E. Kirk. Correlation in the energy markets. In Managing Energy Price Risk, pages 71–78. Risk Publications, 1995. [11] Samuel Kotz, TomaszJ. Kozubowski, and Krzysztof Podgörski. The Laplace Distribution and Generalizations. Springer Science+Business Media, LLC, 1th edition, 2001. [12] SG Kou. A jump-diffusion model for option pricing. In Management Science, volume 48, pages 1086–1101. 2002. [13] Minqiang Li, ShiJie Deng, and JieYun Zhou. Closed-form approximations for spread option prices and greeks. In The Journal of Derivatives, pages 58–80. NewYork, 2008. [14] Chi Fai Lo. Pricing spread options by the operator splitting method. In WILMOTT magazine, pages 64–67. 2015. [15] Kazuhisa Matsuda. Introduction to option pricing with fourier transform: Option pricing with exponential lévy models. In Department of Economics The Graduate Center, The City University of New York. 2004. [16] Robert C. Merton. Option pricing when underlying stock returns are discontinuous. In Journal of Financial Economics, volume 3, pages 125–144. 1976. [17] William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical Recipes in C. Press Syndicate of the University of Cambridge, 2th edition, 2002. [18] Martin Schmelzle. Option pricing formulae using fourier transform: Theory and application. 2010. [19] Siti Maghfirotul Ulyah, Xenos Chang-ShuoLin, and Daniel Wei-Chung Miao. Pricing short-dated foreign equity options with a bivariate jump-diffusion model with correlated fat-tailed jumps. In Finance Research Letters, volume 24, pages 113–128. 2018. [20] Jente Van Belle, Steven Vanduffel, and Jing Yao. Closed-form approximations for spread options in lévy markets. In Applied Stochastic Models in Business and Industry, volume 35. 2018. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/80179 | - |
| dc.description.abstract | 價差選擇權是標的為兩資產的價差的選擇權，投資人可以輕易地透過價差選擇權間接投資兩種資產，因此價差選擇權現今被廣泛應用，如利率、股票、原油及外匯市場等等。然而由於價差選擇權沒有封閉解，因此在訂價及計算希臘字母（Greeks）相對不易。並且過去文獻中多是假設資產服從幾何布朗運動，實證發現，有重大資訊宣布或極端事件發生時，資產價格會有較大的跳動，並且分配呈高峰厚尾形狀，用幾何布朗運動皆無法捕捉此特性，因此本文引用Merton和Kou的跳躍擴散模型，並延伸其隨機過程至雙資產，以針對價差選擇權訂價。除了模型的延伸，本文更是整理了過去被提出的價差選擇權近似方法及數值解，將其延伸至Merton和Kou的跳躍擴散模型下雙資產的評價，從計算精確度及效率比較，在不同模型下找到最適合的訂價引擎。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-23T09:30:24Z (GMT). No. of bitstreams: 1 U0001-2406202116201000.pdf: 4506018 bytes, checksum: a98173dd9fdc1c6a8e2dba43017ca2b5 (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | "Verification Letter from the Oral Examination Committee i Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xiii List of Tables xv Denotation xvii Chapter 1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Chapter 2 Pricing Spread Options under the Black Scholes Model 3 2.1 Introduction of Numerical Integration . . . . . . . . . . . . . . . . . 3 2.1.1 Simpson’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Gauss Hermite Quadrature . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Introduction to Analytical Approximations . . . . . . . . . . . . . . 8 2.2.1 Kirk’s Approximation (1995) . . . . . . . . . . . . . . . . . . . . . 10 2.2.2 Bjerksund and Stensland’s Approximation (2014) . . . . . . . . . . 10 2.2.3 Li, Deng and Zhou’s Approximation (2008) . . . . . . . . . . . . . 12 2.2.4 Lo’s Approximation (2015) . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1 Parameters’ Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Pricing Errors’ Analysis under Existing Approximations . . . . . . 17 2.3.3 Further Investigation of Gauss-Hermite Quadrature . . . . . . . . . 21 2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Chapter 3 Pricing Spread Options under Merton’s Jump-Diffusion Model 27 3.1 Merton’s Jump-Diffusion model . . . . . . . . . . . . . . . . . . . . 28 3.2 Extended Formulas to the Underlying Assets under Merton’s JD . . .29 3.3 Spread Option Pricing Formulas . . . . . . . . . . . . . . . . . . . . 33 3.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4.1 Parameters’ Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4.2 Pricing Errors’ Analysis under Merton’s Jump-Diffusion Model 37 3.4.3 Further Investigation of Gauss-Hermite Quadrature . . . . . . . . . 40 3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Chapter 4 Pricing Spread Options under Kou’s Jump-Diffusion Model 49 4.1 Introduction of Fast Fourier Transform (FFT) . . . . . . . . . . . . . 50 4.1.1 Spread Option Pricing by Two-Dimensional Fourier Transform . . . 52 4.2 Kou’s Jump-Diffusion Model . . . . . . . . . . . . . . . . . . . . . 56 4.3 Bivariate Asymmetric Laplace Jump-Diffusion Model . . . . . . . . 58 4.3.1 Bivariate Asymmetric Laplace Distribution . . . . . . . . . . . . . 58 4.3.2 BALJD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.4.1 Impact of Jump Term . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.4.2 Parameters’ Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . 69 4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Chapter 5 Conclusions and Future Work 73 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 References 75 Appendix A — Bivariate Distributions 79 A.1 Bivariate Normal Distribution (BN) . . . . . . . . . . . . . . . . . . 79 A.2 Bivariate Poisson Distribution (BP) . . . . . . . . . . . . . . . . . . 80 Appendix B — Option Pricing under Jump-Diffusion Models 83 B.1 European Vanilla Call Option . . . . . . . . . . . . . . . . . . . . . 83 Appendix C — Characteristic Function and FFT 85 C.1 Characteristic Function . . . . . . . . . . . . . . . . . . . . . . . . . 85 C.2 Geometric Brownian Motion (GBM) . . . . . . . . . . . . . . . . . 86 C.3 Bivariate Normal Jump-Diffusion (BNJD) . . . . . . . . . . . . . . . 88 C.4 One-Dimensional Fourier Transform . . . . . . . . . . . . . . . . . . 89 C.5 Two-Dimensional FFT . . . . . . . . . . . . . . . . . . . . . . . . . 93 " | |
| dc.language.iso | en | |
| dc.subject | 二元厚尾分配 | zh_TW |
| dc.subject | 跳躍擴散模型 | zh_TW |
| dc.subject | 傅立葉轉換 | zh_TW |
| dc.subject | 近似解析解 | zh_TW |
| dc.subject | 高斯求積 | zh_TW |
| dc.subject | Merton's jump-diffusion model | zh_TW |
| dc.subject | Kou's jump-diffusion Model | zh_TW |
| dc.subject | 價差選擇權 | zh_TW |
| dc.subject | Double Exponential | en |
| dc.subject | double exponential jump-duffusion model | en |
| dc.subject | Merton's jump-diffusion model | en |
| dc.subject | Gauss-Hermite Quadrature | en |
| dc.subject | Analytical Approximation | en |
| dc.subject | Fast Fourier Transform | en |
| dc.subject | Kou's jump-diffusion model | en |
| dc.subject | Bivariate asymmetric Laplace | en |
| dc.subject | Jump-Diffusion model | en |
| dc.subject | Spread option | en |
| dc.title | 價差選擇權在雙資產Merton與Kou的跳躍擴散模型下之評價 | zh_TW |
| dc.title | Pricing Spread Options under Bivariate Merton's and Kou's Jump-Diffusion Models | en |
| dc.date.schoolyear | 109-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 繆維中(Wei-Chung Miao) | |
| dc.contributor.oralexamcommittee | 王之彥(Hsin-Tsai Liu),林昌碩(Chih-Yang Tseng),董夢雲 | |
| dc.subject.keyword | 價差選擇權,跳躍擴散模型,二元厚尾分配,傅立葉轉換,近似解析解,高斯求積,Merton's jump-diffusion model,Kou's jump-diffusion Model, | zh_TW |
| dc.subject.keyword | Spread option,Jump-Diffusion model,Bivariate asymmetric Laplace,Double Exponential,Fast Fourier Transform,Analytical Approximation,Gauss-Hermite Quadrature,Merton's jump-diffusion model,Kou's jump-diffusion model,double exponential jump-duffusion model, | en |
| dc.relation.page | 94 | |
| dc.identifier.doi | 10.6342/NTU202101125 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2021-06-29 | |
| dc.contributor.author-college | 管理學院 | zh_TW |
| dc.contributor.author-dept | 財務金融學研究所 | zh_TW |
| dc.date.embargo-lift | 2023-06-28 | - |
| 顯示於系所單位： | 財務金融學系 | |
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|---|---|---|---|
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