dc.contributor.advisor | 許順吉<br>林士貴 | zh_TW |
dc.contributor.advisor | Sheu, Shuenn-Jyi<br>Lin, Shih-Kuei | en_US |
dc.contributor.author (Authors) | 方麒豪 | zh_TW |
dc.contributor.author (Authors) | Fang, Chi-Hao | en_US |
dc.creator (作者) | 方麒豪 | zh_TW |
dc.creator (作者) | Fang, Chi-Hao | en_US |
dc.date (日期) | 2022 | en_US |
dc.date.accessioned | 1-Aug-2022 18:13:19 (UTC+8) | - |
dc.date.available | 1-Aug-2022 18:13:19 (UTC+8) | - |
dc.date.issued (上傳時間) | 1-Aug-2022 18:13:19 (UTC+8) | - |
dc.identifier (Other Identifiers) | G0109751007 | en_US |
dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/141183 | - |
dc.description (描述) | 碩士 | zh_TW |
dc.description (描述) | 國立政治大學 | zh_TW |
dc.description (描述) | 應用數學系 | zh_TW |
dc.description (描述) | 109751007 | zh_TW |
dc.description.abstract (摘要) | M. Raissi et al.(2019) 首先提出使用監督式學習方法用於求解偏微分方程。他們著重於有封閉解的偏微分方程並且使用封閉解與預測值的差距作為類神經網路的損失函數於訓練中。Lu et al.(2019) 提出更有效率的演算法用於求解多種類型的偏微分方程,包含正演問題以及反演問題。本文將著重於觀察歐式選擇權的類神經網路預測值行為與封閉解的差距並且跟有限差分法進行比較。 | zh_TW |
dc.description.abstract (摘要) | M. Raissi et al.(2019) first proposed a supervised learning method for solving partial differential equations. They focused on partial differential equations that have closed form solutions and used the difference between closed form solutions and neural network outputs as loss function for training. Lu et al.(2019) presented an efficient algorithm for solving several types of partial differential equations, including forward problem and inverse problems. This dissertation aims at observing the behaviour of European call option prices predicted by neural networks and comparing it with closed form price. | en_US |
dc.description.tableofcontents | 中文摘要 iAbstract iiContents iiiList of Tables vList of Figures1 Introduction 12 Literature Review 32.1 Finite Difference 32.2 Neural Network 33 Methodology 53.1 Black-Scholes Partial Differential Equation 53.2 Finite Difference for Black-Scholes PDE 73.3 Merton Partial Integro-Differential Equation 83.4 Finite Difference for Merton PIDE 123.5 Neural Network for Black-Scholes PDE 154 Numerical Results 204.1 Finite Difference 204.1.1 BS PDE 204.1.2 Merton PIDE 214.2 Neural Networks 274.2.1 BS PDE 275 Conclusions 29References 30A Derivation of Black-Scholes Option Price Formula 31B Derivation of Merton Jump Diffusion Model Option Price Formula 33C More Figures and Tables 39 | zh_TW |
dc.format.extent | 654331 bytes | - |
dc.format.mimetype | application/pdf | - |
dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0109751007 | en_US |
dc.subject (關鍵詞) | 類神經網路 | zh_TW |
dc.subject (關鍵詞) | 有限差分法 | zh_TW |
dc.subject (關鍵詞) | Merton 偏積分微分方程 | zh_TW |
dc.subject (關鍵詞) | Black- Scholes 偏微分方程 | zh_TW |
dc.subject (關鍵詞) | 歐式選擇權價格 | zh_TW |
dc.subject (關鍵詞) | Neural Networks | en_US |
dc.subject (關鍵詞) | Finite Difference | en_US |
dc.subject (關鍵詞) | Merton PIDE | en_US |
dc.subject (關鍵詞) | Black-Scholes PDE | en_US |
dc.subject (關鍵詞) | European Call Option Price | en_US |
dc.title (題名) | 選擇權偏微分方程之數值分析: 有限差分法及類神經網路法之應用 | zh_TW |
dc.title (題名) | Numerical Analysis of Option Partial Differential Equations: Applications of Finite Difference and Neural Networks Methods | en_US |
dc.type (資料類型) | thesis | en_US |
dc.relation.reference (參考文獻) | Cont, R., & Voltchkova, E. (2006). A finite difference scheme for option pricing in jumpdiffusion and exponential lévy models. SIAM Journal on Numerical Analysis, 43(4),1596–1626. https://doi.org/10.1137/S0036142903436186Cybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Mathematics ofControl, Signals, and Systems, 2, 303–314. https://doi.org/10.1007/BF02551274Leshno, M., Lin, V. Y., Pinkus, A., & Schocken, S. (1993). Multilayer feedforward networkswith a nonpolynomial activation function can approximate any function. NeuralNetworks, 6(6), 861–867. https://doi.org/10.1016/S0893-6080(05)80131-5Lu, L., Meng, X., Mao, Z., & Karniadakis, G. E. (2021). Deepxde: A deep learning library forsolving differential equations. SIAM Review, 63(1), 208–228. https://doi.org/10.1137/19M1274067Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: Adeep learning framework for solving forward and inverse problems involving nonlinearpartial differential equations. Journal of Computational Physics, 378(1), 686–707. https://doi.org/10.1016/j.jcp.2018.10.045Schwartz, E. (1977). The valuation of warrants: Implementing a new approach. Journal ofFinancial Economics, 4, 79–93. https://doi.org/10.1016/0304-405X(77)90037-X30 | zh_TW |
dc.identifier.doi (DOI) | 10.6814/NCCU202201023 | en_US |