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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
  • [1] Z. Abdollahy, Y. Mahmoudi, A. S. Shamloo, and M. Baghmisheh, Haar Wavelets Method for Time Fractional Riesz Space Telegraph Equation with Separable Solution, Rep. Math. Phys., 89(1) (2022), 81–96.
  • [2] R. Amin, K. Shah, M. Asif, I. Khan, and F. Ullah, An efficient algorithm for numerical solution of fractional integro-differential equations via Haar wavelet, J. Comput. Appl. Math., 381 (2021), 113028.
  • [3] S. Arbabi, A. Nazari, and M. T. Darvishi A two-dimensional Haar wavelets method for solving systems of PDEs, Appl. Math. Comput., 292 (2017), 33-46.
  • [4] I. Aziz and Siraj-ul-Islam, New algorithms for the numerical solution of nonlinear feredholm and volterra integral equations using Haar wavelets, J. Comput. Appl. Math., 239 (2013), 333–345.
  • [5] A. Boggess and F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, Prentice Hall, 2009.
  • [6] F. Bulut, O¨ . Oru¸c, and A. Esen, Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equation, Math. Comput. Simul., 197 (2022), 0378–4754.
  • [7] C. Chen and C. Hsiao, Haar wavelet method for solving lumped and distributed-parameter systems, IEE Proc. Control Theory Appl., 144(1) (1997), 87–94.
  • [8] S. Haq and A. Ghafoor, An efficient numerical algorithm for multi-dimensional time dependent partial differential equations, Comput. Math. with Appl., 8 (2018), 2723–2734.
  • [9] S. Heydary and A. Aminataei, Numerical solution of Drinfel’d–Sokolov system with the Haar wavelets method, Comput. Method Diff. Eq., 10(4) (2022), 1086-1096.
  • [10] D. Hogham, An introduction to financial option valuation: mathematics, stochastics, and computation, Cambridge University Press, 2004.
  • [11] J. Hull, Options, futures, and other derivatives, Pearson, 2018.
  • [12] Y. Khan, M. Ghasemi, S. Vahdati, and M. Fardi, Legendre multi-wavelets to solve oscillating magnetic fields integro-differential equations, U.P.B. Sci. Bull., Series A, 76(1) (2014), 51–58.
  • [13] D. Kumar and K. Deswal, Wavelet-based approximation for two-parameter singularly perturbed problems with Robin boundary conditions, J. Appl. Math. Comput., 68 (2022), 25–149.
  • [14] U. Lepik and H. Hein, Haar Wavelets With Applications, Springer, 2014.
  • [15] S. Pandit, Local radial basis functions and scale-3 Haar wavelets operational matrices based numerical algorithms for generalized regularized long wave model, Wave Motion, 109 (2022), 102846.
  • [16] N. Pervaiz and I. Aziz, Haar wavelet approximation for the solution of cubic nonlinear Schrodinger equations, Phys. A: Stat. Mech. Appl., 545, (2020), 123738.
  • [17] S. Ross, An elementary introduction to mathematical finance, Cambridge University Press, 2011.
  • [18] U. Saeed and M. ur Rehman, Haar wavelet operational matrix method for fractional oscillation equations, Int. J. of Math. Math. Sci., 2014 (2014).
  • [19] R. Singh, V. Guleria and M. Singh, Haar wavelet quasi linearization method for numerical solution of Em- den–Fowler type equations, Math. Comput. Simul., 174 (2020), 123–133.
  • [20] Siraj ul Islam, I. Aziz, and A. S. Al-Fahid, An improved method based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders, J. Comput. Appl. Math., 260 (2014), 449-469.
  • [21] S. E. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004.
  • [22] Swati, M. Singh, and K. Singh, An advancement approach of Haar wavelet method and Bratu-type equations, Appl. Numer. Math., 170 (2021), 74–82.
  • [23] S. Vahdati, A wavelet method for stochastic Volterra integral equations and its application to general stock model, Comput. Method Diff. Eq., 5(2) (2017), 170–188.
  • [24] S. Vahdati and D. Mirzaei, The Finite Points Approximation to the PDE Problems in Multi-Asset Options, CMES- Comput. Model. Eng. Sci., 109-110(3) (2015), 247–262.
  • [25] A. K. Verma, M. K. Rawani and C. Cattani, A numerical scheme for a class of generalized Burgers equation based on Haar wavelet nonstandard finite difference method, Appl. Numer. Math., 168 (2021), 41–54.
  • [26] H. A. Zedan and E. Alaidarous, Haar wavelet method for the system of integral equations, Abstr. Appl. Anal., 2014 (2014).
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