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Conservative Third-Order Central-Upwind Schemes for Option Pricing Problems

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Abstract

In this paper, we propose the application of third-order semi-discrete central-upwind conservative schemes to option pricing partial differential equations (PDEs). Our method is a high-order extension of the recent efficient second-order “Black-Box” schemes that successfully priced several option pricing problems. We consider the Kurganov–Levy scheme and its extensions, namely the Kurganov–Noelle–Petrova and the Kolb schemes. These “Black-Box” solvers ensure non-oscillatory property and achieve desired accuracy using a third-order central weighted essentially non-oscillatory (CWENO) reconstruction. We compare the schemes using a European test case and observe that the Kolb scheme performs better. We apply the Kolb scheme to one-dimensional butterfly, barrier, American and non-linear options under the Black–Scholes model. Further, we extend the Kurganov–Levy scheme to solve two-dimensional convection-dominated Asian PDE. We also price American options under the constant elasticity of variance (CEV) model, which treats volatility as a stochastic instead of a constant as in Black–Scholes model. Numerical experiments achieve third-order, non-oscillatory and high-resolution solutions.

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Acknowledgements

The research of O. Bhatoo was supported by a postgraduate research scholarship from the Tertiary Education Commission. The work of E. Tadmor was supported in part by ONR grant N00014-1812465 and NSF grants RNMS11-07444 (Ki-Net) and DMS-1613911.

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Authors and Affiliations

  1. Department of Applied Mathematical Sciences, University of Technology, Mauritius, La Tour Koenig, 11134, Pointe-aux-Sables, Mauritius

    Omishwary Bhatoo, Arshad Ahmud Iqbal Peer & Aslam Aly El Faidal Saib

  2. Department of Mathematics, Institute for Physical Sciences and Technology (IPST) and Center of Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD, 20742-4015, USA

    Eitan Tadmor

  3. Department of Mathematics, University of Mauritius, Réduit, 80837, Mauritius

    Désiré Yannick Tangman

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  1. Omishwary Bhatoo
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  2. Arshad Ahmud Iqbal Peer
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  3. Eitan Tadmor
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  4. Désiré Yannick Tangman
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  5. Aslam Aly El Faidal Saib
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Correspondence to Eitan Tadmor.

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Bhatoo, O., Peer, A.A.I., Tadmor, E. et al. Conservative Third-Order Central-Upwind Schemes for Option Pricing Problems. Vietnam J. Math. 47, 813–833 (2019). https://doi.org/10.1007/s10013-019-00360-8

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  • DOI: https://doi.org/10.1007/s10013-019-00360-8

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