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Compact Finite Difference Method for Pricing European and American Options Under Jump-Diffusion Models

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Computational Sciences - Modelling, Computing and Soft Computing (CSMCS 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1345))

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Abstract

In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementarity problem governing European and American options respectively are discretized using Crank-Nicolson Leap-Frog scheme. In proposed compact finite difference method, the second derivative is approximated by the value of unknowns and their first derivative approximations which allow us to obtain a tri-diagonal system of linear equations for the fully discrete problem. Further, consistency and stability for the fully discrete problem are also proved. Since jump-diffusion models do not have smooth initial conditions, the smoothing operators are employed to ensure fourth-order convergence rate. Numerical illustrations for pricing European and American options under Merton jump-diffusion model are presented to validate the theoretical results.

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Authors and Affiliations

  1. Dr. SPM International Institute of Information Technology Naya Raipur, Naya Raipur, 493661, Chhattisgarh, India

    Kuldip Singh Patel

  2. Indian Institute of Technology Delhi, New Delhi, 110016, India

    Mani Mehra

Authors
  1. Kuldip Singh Patel
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  2. Mani Mehra
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Correspondence to Kuldip Singh Patel .

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Editors and Affiliations

  1. National Institute of Technology Calicut, Kozhikode, Kerala, India

    Ashish Awasthi

  2. National Institute of Technology Calicut, Kozhikode, Kerala, India

    Sunil Jacob John

  3. National Institute of Technology Calicut, Kozhikode, Kerala, India

    Satyananda Panda

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Patel, K.S., Mehra, M. (2021). Compact Finite Difference Method for Pricing European and American Options Under Jump-Diffusion Models. In: Awasthi, A., John, S.J., Panda, S. (eds) Computational Sciences - Modelling, Computing and Soft Computing. CSMCS 2020. Communications in Computer and Information Science, vol 1345. Springer, Singapore. https://doi.org/10.1007/978-981-16-4772-7_7

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  • DOI: https://doi.org/10.1007/978-981-16-4772-7_7

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-4771-0

  • Online ISBN: 978-981-16-4772-7

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