Numerical methods for early-exercise option pricing via Fourier analysis
University of Macau === Faculty of Science and Technology === Department of Mathematics
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University of Macau
2010
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| Online Access: | http://umaclib3.umac.mo/record=b2148270 |
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ndltd-MACAU-oai-libdigital.umac.mo-b21482702013-01-07T23:06:55Z2010http://umaclib3.umac.mo/record=b2148270UM_THESESUniversity of MacauFaculty of Science and TechnologyDepartment of MathematicsUniversity of MacauUniversity of Macau -- Dissertations澳門大學 -- 論文Options (Finance) -- Mathematical modelsOptions (Finance) -- Prices -- Mathematical modelsFourier analysisMathematics -- Department of MathematicsengHuang, Ning YingNumerical methods for early-exercise option pricing via Fourier analysisThe financial market is developing explosively, although it is struck by the financial 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 Levy 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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NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
University of Macau -- Dissertations 澳門大學 -- 論文 Options (Finance) -- Mathematical models Options (Finance) -- Prices -- Mathematical models Fourier analysis Mathematics -- Department of Mathematics |
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University of Macau -- Dissertations 澳門大學 -- 論文 Options (Finance) -- Mathematical models Options (Finance) -- Prices -- Mathematical models Fourier analysis Mathematics -- Department of Mathematics Huang, Ning Ying Numerical methods for early-exercise option pricing via Fourier analysis |
| description |
University of Macau === Faculty of Science and Technology === Department of Mathematics |
| author |
Huang, Ning Ying |
| author_facet |
Huang, Ning Ying |
| author_sort |
Huang, Ning Ying |
| title |
Numerical methods for early-exercise option pricing via Fourier analysis |
| title_short |
Numerical methods for early-exercise option pricing via Fourier analysis |
| title_full |
Numerical methods for early-exercise option pricing via Fourier analysis |
| title_fullStr |
Numerical methods for early-exercise option pricing via Fourier analysis |
| title_full_unstemmed |
Numerical methods for early-exercise option pricing via Fourier analysis |
| title_sort |
numerical methods for early-exercise option pricing via fourier analysis |
| publisher |
University of Macau |
| publishDate |
2010 |
| url |
http://umaclib3.umac.mo/record=b2148270 |
| work_keys_str_mv |
AT huangningying numericalmethodsforearlyexerciseoptionpricingviafourieranalysis |
| _version_ |
1716478996293615616 |