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Vahdati, Saeed, Ahmadi darani, Mohammad Reza, Ghanei, Mohammad Reza. (1402). Haar wavelet-based valuation method for pricing European options. سامانه مدیریت نشریات علمی, 11(2), 281-290. doi: 10.22034/cmde.2022.52027.2177
Saeed Vahdati; Mohammad Reza Ahmadi darani; Mohammad Reza Ghanei. "Haar wavelet-based valuation method for pricing European options". سامانه مدیریت نشریات علمی, 11, 2, 1402, 281-290. doi: 10.22034/cmde.2022.52027.2177
Vahdati, Saeed, Ahmadi darani, Mohammad Reza, Ghanei, Mohammad Reza. (1402). 'Haar wavelet-based valuation method for pricing European options', سامانه مدیریت نشریات علمی, 11(2), pp. 281-290. doi: 10.22034/cmde.2022.52027.2177
Vahdati, Saeed, Ahmadi darani, Mohammad Reza, Ghanei, Mohammad Reza. Haar wavelet-based valuation method for pricing European options. سامانه مدیریت نشریات علمی, 1402; 11(2): 281-290. doi: 10.22034/cmde.2022.52027.2177

Haar wavelet-based valuation method for pricing European options

Computational Methods for Differential Equations
مقاله 6، دوره 11، شماره 2، تیر 2023، صفحه 281-290    اصل مقاله (916.74 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.52027.2177
نویسندگان
Saeed Vahdati* 1؛ Mohammad Reza Ahmadi darani2؛ Mohammad Reza Ghanei1
1Department of Mathematics, Khansar Campus, University of Isfahan, Iran.
2Department of Applies Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran.
چکیده
A numerical method based on the Haar wavelet is introduced in this study for solving the partial differential equation which arises in the pricing of European options. In the first place, and due to the change of variables, the related partial differential equation (PDE) converts into a forward time problem with a spatial domain ranging from 0 to 1. In the following, the Haar wavelet basis is used to approximate the highest derivative order in the equation concerning the spatial variable. Then the lower derivative orders are approximated using the Haar wavelet basis. Finally, by substituting the obtained approximations in the main PDE and doing some computations using the finite differences approach, the problem reduces to a system of linear equations that can be solved to get an approximate solution. The provided examples demonstrate the effectiveness and precision of the method.
کلیدواژه‌ها
European option؛ Haar wavelet؛ Option pricing
مراجع
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