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Errors in the IMEX-BDF-OS methods for pricing American style options under the jump-diffusion model

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Abstract

The operator splitting method has been effectively applied to jump-diffusion models, and it is also easy to implement because the differential and complementarity restrictions are decoupled and solved separately. Despite their ubiquity, these operator-splitting approaches for jump-diffusion models have no stability and error analysis. In this direction, we performed a priori stability analysis for the implicit–explicit backward difference operator splitting techniques (IMEX-BDF-OS). After the stability analysis, we established the error estimates for IMEX-BDF1-OS and IMEX-BDF2-OS techniques. To validate the theoretical results, numerical evidence of the pricing of American options under Kou’s and Merton’s jump-diffusion models has been shown.

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Acknowledgements

We would like to show our gratitude to the Dr. Lok Pati Tripathi, Department of Mathematics, Indian Institute of Technology Goa, India for sharing his valuable thoughts with us throughout this research. The work of author [Deepak Kumar Yadav] is supported by the University Grants Commission(UGC), India (Student ID-DEC18-416341).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rajiv Gandhi Institute of Petroleum Technology, Jais Amethi, 229304, India

    Deepak Kumar Yadav & Alpesh Kumar

  2. Centre for Data Science, Institute of Technical Education and Research (ITER), Siksha ‘O’ Anusandhan (Deemed to be University), Bhubaneswar, Odisha, India

    Akanksha Bhardwaj

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  1. Deepak Kumar Yadav
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  2. Akanksha Bhardwaj
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  3. Alpesh Kumar
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Correspondence to Alpesh Kumar.

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Yadav, D.K., Bhardwaj, A. & Kumar, A. Errors in the IMEX-BDF-OS methods for pricing American style options under the jump-diffusion model. Comp. Appl. Math. 43, 6 (2024). https://doi.org/10.1007/s40314-023-02510-8

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  • DOI: https://doi.org/10.1007/s40314-023-02510-8

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