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RBF-FD based some implicit-explicit methods for pricing option under regime-switching jump-diffusion model with variable coefficients

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Abstract

In this manuscript, we introduced the radial basis function based three implicit-explicit (IMEX) finite difference techniques for pricing European and American options in an extended Markovian regime-switching jump-diffusion (RSJD) economy. A partial integrodifferential equation (PIDE) yields the values of the European option, which is one of the financial options, and a linear complementary problem (LCP) yields the prices of the American option. To solve the LCP for American option pricing, we combine the suggested techniques with the operator splitting methods. The suggested methods are designed to prevent the use of any fixed-point repetition approaches at each economic stage and time increment. We analyzed the stability of the proposed time discretization methods. We performed numerical experiments and illustrated the second-order convergence and efficiency of the three IMEX numerical techniques (BDF2, CNAB, CNLF) under the extended RSJD model.

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Acknowledgements

Authors would like to thank the anonymous referees for their valuable comments and suggestions, which helped us to improve the exposition of this paper. We would like to show our gratitude to Dr. Lok Pati Tripathi, Department of Mathematics, Indian Institute of Technology Goa, India, for sharing his valuable thoughts with us throughout this research.

Funding

The work of author Deepak Kumar Yadav is supported by the University Grants Commission (UGC), India (Student ID-DEC18-416341), and Rajesh Yadav is supported by the Council of Scientific and Industrial Research, India, with file no. 09/1201(13064)/2022-EMR-I, and the work of author Alpesh Kumar, is supported by the Science and Engineering Research Board, India, under the MATRICS scheme with sanction order number MTR/2022/000149.

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

    Rajesh Yadav & Deepak Kumar Yadav

  2. Department of Mathematics, University of Allahabad, Prayagraj, Uttar Pradesh, 211002, India

    Alpesh Kumar

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  1. Rajesh Yadav
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Contributions

R.Y. has implemented the RBF and generated the numerical results. D.K.Y. gave the conception, stability analysis, and draft of the article. A.K. has done the critical revision of the article and given the approval to be submitted. All authors reviewed the manuscript.

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Correspondence to Deepak Kumar Yadav.

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Yadav, R., Yadav, D.K. & Kumar, A. RBF-FD based some implicit-explicit methods for pricing option under regime-switching jump-diffusion model with variable coefficients. Numer Algor (2023). https://doi.org/10.1007/s11075-023-01719-2

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