Pricing American Options by a Fourier Transform Multinomial Tree in a Conic Market
Based on FFT, a high-order multinomial tree is constructed, and the method to obtain the price of American style options in the Lévy conic market is studied. Firstly, the nature of the Lévy process and the pricing principle of European-style options are introduced. Secondly, the method to construct...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2022/8650500 |
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| author | Weiwei Wang Xiaoping Hu |
| author_facet | Weiwei Wang Xiaoping Hu |
| author_sort | Weiwei Wang |
| collection | DOAJ |
| description | Based on FFT, a high-order multinomial tree is constructed, and the method to obtain the price of American style options in the Lévy conic market is studied. Firstly, the nature of the Lévy process and the pricing principle of European-style options are introduced. Secondly, the method to construct a high-order multinomial tree based on Fourier transform is presented. It can be proved by theoretical derivation that the multinomial tree can converge to the Lévy process. Thirdly, we introduce the conic market theory based on the concave distortion function and give the discretization method of the concave distortion expectation. Then, the American option pricing method based on reverse iteration is given. Finally, the CGMY process is used to demonstrate how to price the American put option in the Lévy conic market. We can draw conclusions that the Fourier transform multinomial tree can avoid the difficulty of parameter estimation when using traditional moment matching methods to construct multinomial trees. Because the Lévy process has the analytic form characteristic function, this method is a promising method to calculate the prices of options in the Lévy conic market. |
| format | Article |
| id | doaj-art-5a43cfac9fb9459d8835fe1555fd8655 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-5a43cfac9fb9459d8835fe1555fd86552025-02-03T01:00:41ZengWileyDiscrete Dynamics in Nature and Society1607-887X2022-01-01202210.1155/2022/8650500Pricing American Options by a Fourier Transform Multinomial Tree in a Conic MarketWeiwei Wang0Xiaoping Hu1School of Applied TechnologySchool of Economics and ManagementBased on FFT, a high-order multinomial tree is constructed, and the method to obtain the price of American style options in the Lévy conic market is studied. Firstly, the nature of the Lévy process and the pricing principle of European-style options are introduced. Secondly, the method to construct a high-order multinomial tree based on Fourier transform is presented. It can be proved by theoretical derivation that the multinomial tree can converge to the Lévy process. Thirdly, we introduce the conic market theory based on the concave distortion function and give the discretization method of the concave distortion expectation. Then, the American option pricing method based on reverse iteration is given. Finally, the CGMY process is used to demonstrate how to price the American put option in the Lévy conic market. We can draw conclusions that the Fourier transform multinomial tree can avoid the difficulty of parameter estimation when using traditional moment matching methods to construct multinomial trees. Because the Lévy process has the analytic form characteristic function, this method is a promising method to calculate the prices of options in the Lévy conic market.http://dx.doi.org/10.1155/2022/8650500 |
| spellingShingle | Weiwei Wang Xiaoping Hu Pricing American Options by a Fourier Transform Multinomial Tree in a Conic Market Discrete Dynamics in Nature and Society |
| title | Pricing American Options by a Fourier Transform Multinomial Tree in a Conic Market |
| title_full | Pricing American Options by a Fourier Transform Multinomial Tree in a Conic Market |
| title_fullStr | Pricing American Options by a Fourier Transform Multinomial Tree in a Conic Market |
| title_full_unstemmed | Pricing American Options by a Fourier Transform Multinomial Tree in a Conic Market |
| title_short | Pricing American Options by a Fourier Transform Multinomial Tree in a Conic Market |
| title_sort | pricing american options by a fourier transform multinomial tree in a conic market |
| url | http://dx.doi.org/10.1155/2022/8650500 |
| work_keys_str_mv | AT weiweiwang pricingamericanoptionsbyafouriertransformmultinomialtreeinaconicmarket AT xiaopinghu pricingamericanoptionsbyafouriertransformmultinomialtreeinaconicmarket |