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Effective implementation of sine-cosine wavelet in pricing discrete double barrier option | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 29، دوره 16، شماره 2، اردیبهشت 2025، صفحه 365-371 اصل مقاله (416.93 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.31435.4629 | ||
| نویسندگان | ||
| Amir Hossein Sobhani* 1؛ Mohammad Hossein Beheshti2 | ||
| 1Department of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran | ||
| 2Department of Biostatistics and Epidemiology, Faculty of Medicine, Tehran Medical Sciences, Islamic Azad University, Tehran, Iran | ||
| تاریخ دریافت: 14 مرداد 1402، تاریخ بازنگری: 04 شهریور 1402، تاریخ پذیرش: 14 آبان 1402 | ||
| چکیده | ||
| In this article, the problem of pricing discrete double barrier options which only monitored at specific times is investigated. According to the Black-Scholes framework, the option price would be obtained from recursively solving the Black-Sholes partial differential equations on the monitoring intervals. In this way, the sine-cosine wavelet approach is applied in approximating the yielded analytical expression. Finally, an operational matrix form is derived which is highly comparable with other methods. According to the method of the present paper, the computational time is nearly fixed against increases in the number of monitoring dates. | ||
| کلیدواژه‌ها | ||
| Barrier Options؛ Black-Scholes Framework؛ sine-cosine Wavelet؛ Orthogonal Projection | ||
| مراجع | ||
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[1] D.-H. Ahn, S. Figlewski, and B. Gao, Pricing discrete barrier options with an adaptive mesh model, J. Derivat. 6 (1999), no. 4, 33. [2] Ph. Anselone and Th. Palmer, Spectral analysis of collectively compact, strongly convergent operator sequences, Pacific J. Math. 25 (1968), no. 3, 423–431. [3] T. Bjork, Arbitrage Theory in Continuous Time, Oxford University Press, 2009. [4] F. Fang and C.W. Oosterlee, A novel pricing method for European options based on Fourier-cosine series expansions, SIAM J. Sci. Comput. 31 (2009), no. 2, 826–848. [5] F. Fang and C.W. Oosterlee, Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions, Numer. Math. 114 (2009), no. 1, 27. [6] R. Farnoosh, A. Sobhani, and M.H. Beheshti, Efficient and fast numerical method for pricing discrete double barrier option by projection method, Comput. Math. Appl. 73 (2017), no. 7, 1539–1545. [7] G. Fusai, I.D. Abrahams, and C. Sgarra, An exact analytical solution for discrete barrier options, Finance Stochast. 10 (2006), no. 1, 1–26. [8] Y.K. Kwok, Mathematical Models of Financial Derivatives, Springer-Verlag, Singapore, 2008. [9] M. Milev and A. Tagliani, Numerical valuation of discrete double barrier options, J. Comput. Appl. Math. 233 (2010), no. 10, 2468–2480. [10] C.-J. Shea, Numerical valuation of discrete barrier options with the adaptive mesh model and other competing techniques, Master’s Thesis, Department of Computer Science and Information Engineering, National Taiwan University, 2005. [11] A. Sobhani and M. Milev, A numerical method for pricing discrete double barrier option by Legendre multiwavelet, J. Comput. Appl. Math. 328 (2018), 355- 364. [12] A. Sobhani and M. Milev, A numerical method for pricing discrete double barrier option by Lagrange interpolation on Jacobi nodes, Math. Meth. Appl. Sci. 46 (2023), no. 5, 6042–6053. [13] W.A. Strauss, Partial Differential Equations: An Introduction, John Wiley & Sons, 2007. [14] S. Yousefi and A. Banifatemi, Numerical solution of Fredholm integral equations by using CAS wavelets, Appl. Math. Comput. 183 (2006), no. 1, 458–463. | ||
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