پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 635 |
| تعداد مقالات | 9,314 |
| تعداد مشاهده مقاله | 67,881,315 |
| تعداد دریافت فایل اصل مقاله | 17,107,965 |
An effective algorithm to solve option pricing problems | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 21، دوره 12، شماره 1، مرداد 2021، صفحه 261-271 اصل مقاله (839.51 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4782 | ||
| نویسنده | ||
| Mojtaba Moradipour* | ||
| Department of Mathematics, Lorestan University, Khorramabad, Iran | ||
| تاریخ دریافت: 28 مرداد 1399، تاریخ بازنگری: 17 آبان 1399، تاریخ پذیرش: 20 آبان 1399 | ||
| چکیده | ||
| We are aimed to develop a fast and direct algorithm to solve linear complementarity problems (LCP's) arising from option pricing problems. We discretize the free boundary problem of American options in temporal direction and obtain a sequence of linear complementarity problems (LCP's) in the finite dimensional Euclidian space $\mathbb{R}^m$. We develop a fast and direct algorithm based on the active set strategy to solve the LCP's. The active set strategy in general needs $O(2^m m^3)$ operations to solve $m$ dimensional LCP's. Using Thomas algorithm, we develop an algorithm with order of complexity $O(m)$ which can extremely speed up the computations. | ||
| کلیدواژه‌ها | ||
| American options؛ variational inequalities؛ linear complementarity problems | ||
| مراجع | ||
|
[1] R.W. Cottle, J.S. Pang and R.E. Stone, The Linear Complementarity Problem, Society for Industrial and Applied Mathematics, 2009. [2] J. Crank, Free and Moving Boundary Problems, Oxford Science Publications, Clarendon Press, 1984. [3] D.J. Duffy, Finite Difference Methods in Financial Engineering, Wiley Finance Series, John Wiley & Sons, Ltd., Chichester, 2006. [4] M.B. Giles and R. Carter, Convergence analysis of Crank-Nicholson and Rannacher time-marching, J. Comput. Finance 9 (2006) 89–112. [5] R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Scientific Computation, Springer Berlin Heidelberg, 2013. [6] P. Hartman and G. Stampacchia, On some non-linear elliptic differential-functional equations, Acta Math. 115(1) (1966) 271–310. [7] A.D. Holmes, A Front-Fixing Finite Element Method for the Valuation of American Options, PhD thesis, University of Nevada, Las Vegas, 2010. [8] S. Ikonen and J. Toivanen, Pricing American options using LU decomposition, Appl. Math. Sci. (Ruse) 1(49-52) (2007) 2529–2551. [9] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000. [10] M. Moradipour and S.A. Yousefi, Using spectral element method to solve variational inequalities with applications in finance, Chaos, Solitons Fractals 81 (2015) 208–217. [11] J.L. Morales, J. Nocedal and M. Smelyanskiy, An algorithm for the fast solution of symmetric linear complementarity problems, Numer. Math. 111(2) (2008) 251–266. [12] R. Rannacher, Finite element solution of diffusion problems with irregular data, Numerische Math. 43(2) (1984) 309–327. [13] R.U. Seydel, Tools for Computational Finance, Universitext Springer-Verlag, Berlin, Fourth Edition, 2009. [14] J. Toivanen, Numerical valuation of European and American options under Kou’s jump-diffusion model, SIAM J. Sci. Comput. 30(4) (2008) 1949–1970. | ||
|
آمار تعداد مشاهده مقاله: 15,605 تعداد دریافت فایل اصل مقاله: 2,316 |
||