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Two-Grid Decoupled Method for a Black-Scholes Increased Market Volatility Model

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Numerical Methods and Applications (NMA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8962))

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Abstract

In this paper we consider a pricing model that predicts increased implied volatility with minimal assumptions beyond those of the Black-Scholes theory. It is described by systems of nonlinear Black-Scholes equations. We propose a two-grid algorithm that consists of two steps: solving the coupled Partial Differential Equations (PDEs) problem on a coarse grid and then solving a number of decoupled sub-problems on a fine mesh by using the coarse grid solution to linearise each PDE of the system. Numerical experiments illustrate the efficiency of the method and validate the related theoretical analysis.

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Acknowledgement

This research was supported by the European Commission under Grant Agreement number 304617 (FP7 Marie Curie Action Project Multi-ITN STRIKE - Novel Methods in Computational Finance) and Bulgarian National Fund of Science under Project DID 02/37-2009.

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Authors and Affiliations

  1. Faculty of Natural Science and Education, University of Ruse, 8 Studentska Street, 7017, Ruse, Bulgaria

    Miglena N. Koleva & Lubin G. Vulkov

Authors
  1. Miglena N. Koleva
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  2. Lubin G. Vulkov
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Corresponding author

Correspondence to Miglena N. Koleva .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

  3. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

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Koleva, M.N., Vulkov, L.G. (2015). Two-Grid Decoupled Method for a Black-Scholes Increased Market Volatility Model. In: Dimov, I., Fidanova, S., Lirkov, I. (eds) Numerical Methods and Applications. NMA 2014. Lecture Notes in Computer Science(), vol 8962. Springer, Cham. https://doi.org/10.1007/978-3-319-15585-2_30

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  • DOI: https://doi.org/10.1007/978-3-319-15585-2_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15584-5

  • Online ISBN: 978-3-319-15585-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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