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Pricing European Options under Jump Diffusion Models with Fast L-stable Padé Scheme
The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.
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[1] R. C. Merton, “Option pricing when underlying stock returns are discontinuous,” Journal of financial economics, vol. 3, no. 1-2, pp. 125–144, 1976.
[2] S. G. Kou, “A jump-diffusion model for option pricing,” Management science, vol. 48, no. 8, pp. 1086–1101, 2002.
[3] L. Andersen and J. Andreasen, “Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing,” Review of Derivatives Research, vol. 4, no. 3, pp. 231–262, 2000.
[4] K. J. in’t Hout and J. Toivanen, “Adi schemes for valuing european options under the bates model,” Applied Numerical Mathematics, vol. 130, pp. 143–156, 2018.
[5] K. I. Amin, “Jump diffusion option valuation in discrete time,” The journal of finance, vol. 48, no. 5, pp. 1833–1863, 1993.
[6] S. Zhang, “Radial basis functions method for valuing options: A multinomial tree approach,” Journal of Computational and Applied Mathematics, vol. 319, pp. 97–107, 2017.
[7] N. Cantarutti and J. Guerra, “Multinomial method for option pricing under variance gamma,” International Journal of Computer Mathematics, vol. 96, no. 6, pp. 1087–1106, 2019.
[8] A. Almendral and C. W. Oosterlee, “Numerical valuation of options with jumps in the underlying,” Applied Numerical Mathematics, vol. 53, no. 1, pp. 1–18, 2005.
[9] A. Itkin, “Efficient solution of backward jump-diffusion partial integro-differential equations with splitting and matrix exponentials,” Journal of Computational Finance, vol. 19, no. 3, 2016.
[10] L. Boen et al., “Operator splitting schemes for the two-asset merton jump–diffusion model,” Journal of Computational and Applied Mathematics, 2019.
[11] A. Khaliq, B. Wade, M. Yousuf, and J. Vigo-Aguiar, “High order smoothing schemes for inhomogeneous parabolic problems with applications in option pricing,” Numerical Methods for Partial Differential Equations, vol. 23, no. 5, pp. 1249–1276, 2007.
[12] Y. dHalluin, P. A. Forsyth, and G. Labahn, “A penalty method for american options with jump diffusion processes,” Numerische Mathematik, vol. 97, no. 2, pp. 321–352, 2004.
[13] S. Cox and P. Matthews, “Exponential time differencing for stiff systems,” Journal of Computational Physics, vol. 176, no. 2, pp. 430–455, 2002.
[14] A.-K. Kassam and L. N. Trefethen, “Fourth-order time-stepping for stiff pdes,” SIAM Journal on Scientific Computing, vol. 26, no. 4, pp. 1214–1233, 2005.
[15] A. Khaliq, J. Martin-Vaquero, B. Wade, and M. Yousuf, “Smoothing schemes for reaction-diffusion systems with nonsmooth data,” Journal of Computational and Applied Mathematics, vol. 223, no. 1, pp. 374–386, 2009.
[16] A. Khaliq, E. Twizell, and D. Voss, “On parallel algorithms for semidiscretized parabolic partial differential equations based on subdiagonal pad´e approximations,” Numerical Methods for Partial Differential Equations, vol. 9, no. 2, pp. 107–116, 1993.
[17] E. Gallopoulos and Y. Saad, “On the parallel solution of parabolic equations,” in Proceedings of the 3rd international conference on Supercomputing, pp. 17–28, ACM, 1989.
[18] G. Beylkin, J. M. Keiser, and L. Vozovoi, “A new class of time discretization schemes for the solution of nonlinear pdes,” Journal of computational physics, vol. 147, no. 2, pp. 362–387, 1998.
[19] C. R. Vogel, Computational methods for inverse problems, vol. 23. Siam, 2002.
[20] N. Rambeerich, D. Tangman, A. Gopaul, and M. Bhuruth, “Exponential time integration for fast finite element solutions of some financial engineering problems,” Journal of Computational and Applied Mathematics, vol. 224, no. 2, pp. 668–678, 2009.
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