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An efficient numerical method for the valuation of American multi-asset options

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Abstract

In this paper, a fast and efficient numerical method which relies on the far field truncation technique, the finite element discretization, and the projection contraction method (PCM) is proposed for pricing American multi-asset options. It is well known that American multi-asset option satisfies a linear complementarity problem (LCP), which is a multi-dimensional variable coefficient parabolic model on an unbounded domain. First, we transform it into a constant coefficient parabolic LCP on a bounded domain by some skillful transformations and far-field boundary estimate. Then, the variational inequality (VI) corresponding to the truncated LCP is obtained. Further, it is discretized by the finite element method and the implicit difference method in spatial and temporal directions, respectively. Based on the symmetric positive definiteness of the full-discrete matrix, the discretized VI is solved by the PCM. Finally, numerical simulations are provided to verify the efficiency of the proposed method.

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Acknowledgements

The work of Q. Zhang was supported by the Key Programs of Liaoning Province Natural Science Foundation (no. 20170520014). The work of H. Song was supported by the National Natural Science Foundation of China (no. 11701210), the Education Department Project of Jilin Province (no. JJKH20180113KJ), the Science and Technology Department Project of Jilin Province (no. 20190103029JH), and the Fundamental Research Funds for the Central Universities. The authors also wish to thank the Key Laboratory of Symbolic Computation and Knowledge Engineering Ministry of Education, the High Performance Computing Center of Jilin University and the Computing Center of Jilin Province for essential computing support.

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Authors and Affiliations

  1. School of Science, Shenyang University of Technology, Shenyang, 110807, China

    Qi Zhang & Fangfang Wu

  2. Department of Mathematics, Jilin University, Changchun, 130012, China

    Haiming Song & Chengbo Yang

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  1. Qi Zhang
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  2. Haiming Song
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  3. Chengbo Yang
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  4. Fangfang Wu
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Correspondence to Haiming Song.

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Zhang, Q., Song, H., Yang, C. et al. An efficient numerical method for the valuation of American multi-asset options. Comp. Appl. Math. 39, 240 (2020). https://doi.org/10.1007/s40314-020-01290-9

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  • DOI: https://doi.org/10.1007/s40314-020-01290-9

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