Bergische Universität Wuppertal Fachbereich Mathematik und Naturwissenschaften Angewandte Mathematik - Numerische Analysis

People Research Publications Teaching

---

Meshfree Methods in Option Pricing

Masterarbeit Wirtschaftsmathematik

Master's Thesis in Financial Mathematics, Halmstad University, Sweden

Supervision

• Prof. Dr. Matthias Ehrhardt

Description

Keywords

References:

1. A. Belova, M. Ehrhardt and T. Shmidt, Meshfree Methods in Option Pricing, Proceedings of the Mediterranean Conference on Embedded Computing, June 19-21, 2012, Bar, Montenegro, Advances and Challenges in Embedded Computing Vol. 1 (2012), pp. 242-245.
2. G.E. Fasshauer, A.Q.M. Khaliq, D.A. Voss, Using Meshfree Approximation for Multi-Asset American Options, J. Chinese Inst. Eng. 27 (2004), 563-571.
3. G.E. Fasshauer, A.Q.M. Khaliq, D.A. Voss, A parallel time stepping approach using meshfree approximations for pricing options with non-smooth payoffs, J. Chinese Inst. Eng. 27 (2004), 563-571.
4. G.E. Fasshauer, Meshfree approximation methods with MATLAB, World Scientific, 2007.
5. B. Fornberg, E. Lehto, Stabilization of RBF-generated finite difference methods for convective PDEs, J. Comput. Phys. 230 (2011), 2270-2285.
6. B. Fornberg, E. Larsson, N. Flyer, Stable computations with Gaussian radial basis functions, SIAM J. Sci. Comput. 33 (2011), 869-892.
7. M. Griebel, M.A. Schweitzer (eds.), Meshfree Methods for Partial Differential Equations V, Lecture Notes in Computational Science and Engineering 79, Springer, 2011.
8. Y. Goto, Z. Fei, S. Kan, E. Kita, Options valuation by using radial basis function approximation, Engrg. Anal. Bound. Elem. 31 (2007), 836-843.
9. A. Hall, Pricing financial derivatives using radial basis functions and the generalized Fourier transform, UPTEC Report IT 05 036, School of Engineering, Uppsala University, Sweden, 2005.
10. Y.C. Hon, A quasi-radial basis functions method for American options pricing, Comput. Math. Appl. 43 (2002), 513-524.
11. Y.C. Hon, X.C. Mao, A radial basis function method for solving options pricing model, J. Financial Engineering 8 (1999), 1-24.
12. M.B. Koc, I. Boztosum, D. Boztosum, On the numerical solution of Black-Scholes equation, In: Proceedings of International Workshop on Meshfree Method 2003, pp. 11-6.
13. E. Larsson, K. Åhlander, A. Hall, Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform, J. Comput. Appl. Math. 222 (2008), 175-192
14. G. Marcusson, Option pricing using radial basis functions, UPTEC Report F 04 078, School of Engineering, Uppsala University, 2004.
15. U. Pettersson, E. Larsson, G. Marcusson, J. Persson, Option Pricing using Radial Basis Functions, ECCOMAS Thematic Conference on Meshless Methods 2005.
16. U. Pettersson, E. Larsson, G. Marcusson, J. Persson, Improved radial basis function methods for multi-dimensional option pricing, J. Comput. Appl. Math. 222 (2008), 82-93.
17. M.J.D. Powell, The Theory of Radial Basis Function Approximation, Advances in Numerical Analysis III, Oxford: Clarendon Press, 1992, p. 105.
18. M. D. Marcozzi, S. Choi, and C. S. Chen, RBF and optimal stopping problems; an application to the pricing of vanilla options on one risky asset, Boundary Element Technology XIV, C.S. Chen et al. (eds.), Computational Mechanics Publications, (1999), 345-354.
19. S. Rippa, An algorithm for selecting a good value for the parameter c in radial basis function interpolation, Adv. Comput. Math. 11 (1999), 193-210.
20. Z. Wu, Y.C. Hon, Convergence error estimate in solving free boundary diffusion problem by radial basis functions method, Engrg. Anal. Bound. Elem. 27 (2003), 73-79.
21. Z. Wu, Compactly Supported Positive Definite Radial Functions, J. Adv. Comput. Math. 4 (1995), 283.