針對Lévy過程下的二維期權定價問題，本文提出了一種基於快速傅利葉變換(FFT)的解決方案，稱之為二維快速傅利葉變換網絡。不論是時間從屬還是線性組合，此方法適用於所有能取得聯合特徵函數的二維Lévy構建。快速傅利葉變換的種種優點使得比數值方法在不影響結果精確性的前提下，大大降低了所需計算時間。理論上，更高維的Lévy期權定價問題也可以通過擴展數值網絡解決。除此之外，我們還探究了資產波動性亦服從Lévy過程的單資產期權定價。這種資產價值和波動性由一組相關Lévy過程驅動的模型被稱為時間轉換Lévy過程。最後，關於美式及奇異期權定價的數值算例驗證了文中方法的準確性和有效性。 / We propose a two-dimensional network to retrieve the price of two-asset option under Lévy processes by using the fast Fourier transform (FFT). It can be applied to different multivariate Lévy constructions such as subordination and linear combination provided that the joint characteristic function is obtainable. With the prevalent implementation of FFT, the network approach results in significant computational time reduction while maintaining satisfactory accuracy. In general, multi-dimensional option pricing problems are also solvable by extending this network. Furthermore, we investigate option pricing on a single asset where the asset return and its volatility are driven by a pair of dependent Lévy processes. Such a model is also called the random time-changed Lévy process. Numerical examples are given to demonstrate the efficiency and accuracy of FFT-network applied to exotic and American-style options. / Detailed summary in vernacular field only. / Wang, Weiyin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 41-43). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / List of Tables --- p.ii / List of Figures --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.4 / Chapter 2.1 --- Lévy Process --- p.4 / Chapter 2.1.1 --- Definition and Properties --- p.4 / Chapter 2.1.2 --- Multivariate Lévy Construction --- p.6 / Chapter 2.2 --- Fast Fourier Transform (FFT) in Option Pricing --- p.9 / Chapter 2.2.1 --- European Option on One Asset --- p.9 / Chapter 2.2.2 --- European Option on Two Assets --- p.11 / Chapter 3 --- Two-dimensional FFT-network Model --- p.13 / Chapter 3.1 --- Two-dimensional FFT-network --- p.15 / Chapter 3.2 --- Two-asset Option Pricing --- p.22 / Chapter 3.2.1 --- General Model --- p.22 / Chapter 3.2.2 --- Specific Models --- p.23 / Chapter 3.3 --- Random Time-changed Lévy Process --- p.25 / Chapter 3.3.1 --- Model --- p.26 / Chapter 3.3.2 --- Correlation Adjustment --- p.28 / Chapter 4 --- Numerical Examples --- p.31 / Chapter 4.1 --- Two-asset Option --- p.31 / Chapter 4.1.1 --- Spread Option Pricing --- p.31 / Chapter 4.1.2 --- Pricing under Diffierent Multivariate Lévy Constructions --- p.36 / Chapter 4.2 --- One-asset Option under Random Time-changed Lévy Process --- p.37 / Chapter 5 --- Conclusion --- p.40 / Bibliography --- p.41
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328086 |
| Date | January 2013 |
| Contributors | Wang, Weiyin., Chinese University of Hong Kong Graduate School. Division of Risk Management Science. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource ([2], iv, 43 leaves) : ill. (some col.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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