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Numerical methods for early-exercise option pricing via Fourier analysis

English Abstract

The financial market is developing explosively, although it is struck by the fi- nancial tsunami recently. Many new financial derivatives, including options, warrants and swaps are springing out. They are widely used as risk management tool by investors, stock brokers and bankers. But still, options are the most popular derivative products as hedging tools in constructing a portfolio. Recently, Fang and Oosterlee approved a new numerical method for European option pricing which is based on the Fourier-cosine series, and called it the COS method. Then, they applied the COS method on early-exercise and discretely-monitored barrier option pricing. The main work of this thesis is developing the COS method and FFT to price Bermudan Barrier options. Some numerical experiments are done, and it works well under exponential L´evy asset price models. In Chapter 1, Section 1.1, some basic introductions of options are given. In section 1.2, three different kind of options are introduced. In section 1.3, the mathematical background are presented. In Chapter 2, we summarize the Fang and Oosterlee’s method, and show the derivation and the algorithm for European Option, Bermudan Option and Barrier Option in Section 2.1, Section 2.2 and Section 2.3, respectively. In Chapter 3, Section 3.1, we give the definition of Bermudan Barrier Option and derive the mathematical method to price it. In section 3.2, the corresponding algorithms are listed. This is the main work of the thesis. In Chapter 4, Section 4.1, we do numerical experiments on pricing Bermudan Barrier Option. In section 4.2, some conclusions are summarized.

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Huang, Ning Ying


Faculty of Science and Technology


Department of Mathematics




Options (Finance) -- Mathematical models

Options (Finance) -- Prices -- Mathematical models

Fourier analysis


Ding, Deng

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