IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v285y2016icp41-50.html
   My bibliography  Save this article

A new stability result for the modified Craig–Sneyd scheme applied to two-dimensional convection–diffusion equations with mixed derivatives

Author

Listed:
  • Mishra, Chittaranjan

Abstract

The Modified Craig–Sneyd scheme is an alternating direction implicit(ADI) type scheme that was introduced by In ’t Hout and Welfert (2009) [12] in order to numerically solve multidimensional convection–diffusion equations with mixed-derivative terms. It is one of the most prominent ADI schemes currently known for their efficiency in solving above type of problems. This paper deals with a useful stability result for the Modified Craig–Sneyd scheme when applied to two-dimensional convection–diffusion equations with mixed derivative term. The stability of the scheme is analyzed in the von Neumann framework, effectively taking into account the actual size of the mixed derivative term. This study is relevant to an observation of apparent discrepancy in a real world application of the scheme, i.e., in computational finance. The obtained results not only generalize some of the existing stability results, but also clearly justify this surprising observation theoretically.

Suggested Citation

  • Mishra, Chittaranjan, 2016. "A new stability result for the modified Craig–Sneyd scheme applied to two-dimensional convection–diffusion equations with mixed derivatives," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 41-50.
    • Handle: RePEc:eee:apmaco:v:285:y:2016:i:c:p:41-50
    DOI: 10.1016/j.amc.2016.03.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316302156
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.03.022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tinne Haentjens & Karel J. in 't Hout, 2015. "ADI Schemes for Pricing American Options under the Heston Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 207-237, July.
    2. in 't Hout, K.J. & Mishra, C., 2011. "Stability of the modified Craig–Sneyd scheme for two-dimensional convection–diffusion equations with mixed derivative term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2540-2548.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ghosh, Abhijit & Mishra, Chittaranjan, 2021. "Highly efficient parallel algorithms for solving the Bates PIDE for pricing options on a GPU," Applied Mathematics and Computation, Elsevier, vol. 409(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lynn Boen & Karel J. in 't Hout, 2019. "Operator splitting schemes for American options under the two-asset Merton jump-diffusion model," Papers 1912.06809, arXiv.org.
    2. Karel in 't Hout & Jari Toivanen, 2015. "Application of Operator Splitting Methods in Finance," Papers 1504.01022, arXiv.org.
    3. Kathrin Glau & Daniel Kressner & Francesco Statti, 2019. "Low-rank tensor approximation for Chebyshev interpolation in parametric option pricing," Papers 1902.04367, arXiv.org.
    4. Karel in 't Hout & Pieter Lamotte, 2022. "Efficient numerical valuation of European options under the two-asset Kou jump-diffusion model," Papers 2207.10060, arXiv.org, revised May 2023.
    5. Karel in 't Hout & Radoslav Valkov, 2016. "Numerical study of splitting methods for American option valuation," Papers 1610.09622, arXiv.org.
    6. Andersson, Kristoffer & Oosterlee, Cornelis W., 2021. "A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    7. Yiannis A. Papadopoulos & Alan L. Lewis, 2018. "A First Option Calibration of the GARCH Diffusion Model by a PDE Method," Papers 1801.06141, arXiv.org.
    8. Tber, Moulay Hicham, 2023. "A semi-Lagrangian mixed finite element method for advection–diffusion variational inequalities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 202-215.
    9. Maarten Wyns & Karel in 't Hout, 2016. "An adjoint method for the exact calibration of Stochastic Local Volatility models," Papers 1609.00232, arXiv.org.
    10. Karel J. in’t Hout & Jacob Snoeijer, 2021. "Numerical Valuation of American Basket Options via Partial Differential Complementarity Problems," Mathematics, MDPI, vol. 9(13), pages 1-17, June.
    11. Maryam Safaei & Abodolsadeh Neisy & Nader Nematollahi, 2018. "New Splitting Scheme for Pricing American Options Under the Heston Model," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 405-420, August.
    12. Karel in 't Hout & Jacob Snoeijer, 2021. "Numerical valuation of American basket options via partial differential complementarity problems," Papers 2106.01200, arXiv.org.
    13. Kim, See-Woo & Kim, Jeong-Hoon, 2018. "Analytic solutions for variance swaps with double-mean-reverting volatility," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 130-144.
    14. Andersson, Kristoffer & Oosterlee, Cornelis W., 2021. "Deep learning for CVA computations of large portfolios of financial derivatives," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    15. Cornelis S. L. de Graaf & Drona Kandhai & Christoph Reisinger, 2016. "Efficient exposure computation by risk factor decomposition," Papers 1608.01197, arXiv.org, revised Feb 2018.
    16. Yangyang Zhuang & Pan Tang, 2023. "Pricing of American Parisian option as executive option based on the least‐squares Monte Carlo approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(10), pages 1469-1496, October.
    17. Kathrin Glau & Mirco Mahlstedt & Christian Potz, 2018. "A new approach for American option pricing: The Dynamic Chebyshev method," Papers 1806.05579, arXiv.org.
    18. Slobodan Milovanovi'c, 2018. "Pricing Financial Derivatives using Radial Basis Function generated Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts," Papers 1808.02365, arXiv.org, revised Aug 2018.
    19. Blessing Taruvinga & Boda Kang & Christina Sklibosios Nikitopoulos, 2018. "Pricing American Options with Jumps in Asset and Volatility," Research Paper Series 394, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. Reza Mollapourasl & Ali Fereshtian & Michèle Vanmaele, 2019. "Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 259-287, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:285:y:2016:i:c:p:41-50. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.