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Wavelet analytical method on the Heston option pricing model | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 15، دوره 13، شماره 2، مهر 2022، صفحه 151-158 اصل مقاله (457.2 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.24147.2681 | ||
| نویسندگان | ||
| Fereshteh Goldoust* 1؛ Jafar Biazar2 | ||
| 1Department of Applied Mathematics, Islamic Azad University, Bandar Anzali Branch, Anzali, Iran | ||
| 2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan 41335-1914,Rasht, Guilan, Iran | ||
| تاریخ دریافت: 13 مرداد 1400، تاریخ پذیرش: 05 بهمن 1400 | ||
| چکیده | ||
| In this paper, the Heston partial differential equation option pricing model is considered and the Legendre wavelet method (LWM) is used to solve this equation. The attributes of Legendre wavelets are used to reduce the PDEs problem into the solution of the ODEs system. The wavelet base is used in approximation due to its simplicity and efficiency. The method of creating Legendre wavelets and their main properties were briefly mentioned. Some numerical schemes have been compared with the LWM in the result. | ||
| کلیدواژه‌ها | ||
| Keywords: partial and stochastic differential equation؛ Heston model؛ Legendre wavelet method | ||
| مراجع | ||
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[1] R.J. Adler, The Geometry of Random Fields, Wiley & Sons, 1981. [2] H. Albercher, P.Mayer, W. Schoutens and J, Tistaert, The little Heston trap, Wilmot Magazine, January (2007), 83–92. [3] A.F. Atiya and S. Wall, An analytic approximation of the likelihood function for the Heston model volatility estimation problem, Quant. Finance 9 (2009), 289—296. [4] G. Bakshi, C. Cao and Z. Chen, Empirical performance of alternative option pricing models, J. Finance 52 (1997), no. 5, 2003–2049. [5] G. Bakshi and D. Madan, Spanning and derivative-security valuation, J. Financ. Econ. 55 (2000), 205–238. [6] D. Bates, Statistical methods in Finance, vol. 14, p. 567-611, Elsevier, Amsterdam: North Holland, 1996. [7] J. Biazar, E. Babolian, A. Nouri and R. Islam, An alternate algorithm for computing Adomian decomposition method in special cases, Appl. Math. Comput. 138 (2003), 1—7. [8] J.Biazar, F. Goldoust and F. Mehrdoust, On the numerical solutions of Heston partial differential equation, Math. Sci. Lett. 4 (2015), no. 1, 63–68. [9] J. Biazar, M. Tango, E. Babolian and R. Islam, Solution of the kinetic modeling of lactic acid fermentation using Adomian decomposition method, Appl. Math. Comput. 139 (2003), 249—258. [10] J.S. Gu and W.S. Jiang, The Haar Wavelets operational matrix of integration, Int. J. Syst. Sci. 27 (1996), 623–628. [11] S.L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev. Financ. Stud. 6 (1993), 327-343. [12] H. Johnson and D. Shanno, Option pricing when the variance is changing, J. Financ. Quant. Anal. 22 (1987), 143–151. [13] R.Y. Chang and M.L. Wang, Shifted Legendre directs method for variational problems, J. Optim. Theory Appl. 39 (1983), 22–307. [14] C. Peter and D. Madan, Option pricing and the fast Fourier transform, J. Comput. Finance 2 (1999), no. 4, 61–73. [15] M. Razzaghi, Fourier series direct method for variational problems, Int. J. Control 48 (1998), 887–895. [16] ] M. Razzaghi and S. Yousefi, Legendre wavelets direct method for variational problems, Math. Comput. Simul. 53 (2000), 185–192. | ||
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