政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/141183
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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/141183


    Title: 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
    Numerical Analysis of Option Partial Differential Equations: Applications of Finite Difference and Neural Networks Methods
    Authors: 方麒豪
    Fang, Chi-Hao
    Contributors: 許順吉
    林士貴
    Sheu, Shuenn-Jyi
    Lin, Shih-Kuei
    方麒豪
    Fang, Chi-Hao
    Keywords: 類神經網路
    有限差分法
    Merton 偏積分微分方程
    Black- Scholes 偏微分方程
    歐式選擇權價格
    Neural Networks
    Finite Difference
    Merton PIDE
    Black-Scholes PDE
    European Call Option Price
    Date: 2022
    Issue Date: 2022-08-01 18:13:19 (UTC+8)
    Abstract: 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。
    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.
    Reference: Cont, R., & Voltchkova, E. (2006). A finite difference scheme for option pricing in jump
    diffusion and exponential lévy models. SIAM Journal on Numerical Analysis, 43(4),
    1596–1626. https://doi.org/10.1137/S0036142903436186
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    with a nonpolynomial activation function can approximate any function. Neural
    Networks, 6(6), 861–867. https://doi.org/10.1016/S0893-6080(05)80131-5
    Lu, L., Meng, X., Mao, Z., & Karniadakis, G. E. (2021). Deepxde: A deep learning library for
    solving differential equations. SIAM Review, 63(1), 208–228. https://doi.org/10.1137/
    19M1274067
    Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A
    deep learning framework for solving forward and inverse problems involving nonlinear
    partial differential equations. Journal of Computational Physics, 378(1), 686–707. https:
    //doi.org/10.1016/j.jcp.2018.10.045
    Schwartz, E. (1977). The valuation of warrants: Implementing a new approach. Journal of
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    30
    Description: 碩士
    國立政治大學
    應用數學系
    109751007
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0109751007
    Data Type: thesis
    DOI: 10.6814/NCCU202201023
    Appears in Collections:[Department of Mathematical Sciences] Theses

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