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

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• 作者：Zhiqiang Zhou ; Jingtang Ma
• 关键词：Exotic option pricing ; lattice Boltzmann method ; Chapman ; Enskog multi ; scale expansion ; stability ; computational complexity ; 91G20 ; 91G60 ; 91G80
• 刊名：Frontiers of Mathematics in China
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：11
• 期：1
• 页码：237-254
• 全文大小：285 KB
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• 作者单位：Zhiqiang Zhou (1)
  Jingtang Ma (1)
  
  1. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-3576

文摘

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. Keywords Exotic option pricing lattice Boltzmann method Chapman-Enskog multi-scale expansion stability computational complexity