Pricing American options by a Fourier transform multinomial tree in a conic market
type: Item
instance of: scholarly article
title: Pricing American options by a Fourier transform multinomial tree in a conic market
zbMATH Open document ID: 1499.91178
DOI: 10.1155/2022/8650500
author: Xiaoping Hu
author: Weiwei Wang
published in: Discrete Dynamics in Nature and Society
publication date: 2022-10-21T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60G51
zbMATH DE Number: 7605672
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2022/8650500
OpenAlex ID: W4297105439
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description: scientific article; zbMATH DE number 7605672