Lattice Boltzmann methods for solving partial differential equations of exotic option pricing

doi:10.1007/s11464-015-0500-0

Frontiers of Mathematics in China

2016, Vol. 11

Issue (1): 237-254 https://doi.org/10.1007/s11464-015-0500-0

本期目录

Lattice Boltzmann methods for solving partial differential equations of exotic option pricing

Zhiqiang ZHOU,Jingtang MA(

)

School of Economic Mathematics, Southwestern University of Finance and Economics,Chengdu

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Abstract：

This paper establishes a lattice Boltzmann method (LBM) with two amending functions for solving partial differential equations (PDEs) arising in Asian and lookback options pricing. The time evolution of stock prices can be regarded as the movement of randomizing particles in different directions, and the discrete scheme of LBM can be interpreted as the binomial models. With the Chapman-Enskog multi-scale expansion, the PDEs are recovered correctly from the continuous Boltzmann equation and the computational complexity is O(N), where N is the number of space nodes. Compared to the traditional LBM, the coefficients of equilibrium distribution and amending functions are taken as polynomials instead of constants. The stability of LBM is studied via numerical examples and numerical comparisons show that the LBM is as accurate as the existing numerical methods for pricing the exotic options and takes much less CPU time.

Key words： Exotic option pricing lattice Boltzmann method Chapman-Enskog multi-scale expansion stability computational complexity

收稿日期: 2015-02-04 出版日期: 2015-12-02

Corresponding Author(s): Jingtang MA

引用本文:

. [J]. Frontiers of Mathematics in China, 2016, 11(1): 237-254.
Zhiqiang ZHOU,Jingtang MA. Lattice Boltzmann methods for solving partial differential equations of exotic option pricing. Front. Math. China, 2016, 11(1): 237-254.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.1007/s11464-015-0500-0
https://academic.hep.com.cn/fmc/CN/Y2016/V11/I1/237

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