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A Numerical Method for Pricing Discrete Double Barrier Option by Lagrange Interpolation on Jacobi Nodes
  • Amirhossein Sobhani,
  • mariyan milev
Amirhossein Sobhani
Semnan University

Corresponding Author:[email protected]

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mariyan milev
University of Food Technology-Plovdiv, Head of Mathematics and Physics Bulgaria, Plovdiv.
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In this paper, a rapid and high accurate numerical method for pricing discrete single and double barrier knock-out call options is presented. With regard to the well-known Black-Scholes model, the price of an option in each monitoring date could be calculated by computing a recursive integral formula that is based on the heat equation solution. We have approximated these recursive solutions with the aid of Lagrange interpolation on Jacobi polynomial nodes. After that, an operational matrix, that makes our computation significantly fast, has been derived. In some theorems, the convergence of the presented method has been shown and the rate of convergence has been derived. The most important benefit of this method is that its complexity is very low and does not depend on the number of monitoring dates. The numerical results confirm the accuracy and efficiency of the presented numerical algorithm.
27 May 2021Submitted to Mathematical Methods in the Applied Sciences
11 Jun 2021Submission Checks Completed
11 Jun 2021Assigned to Editor
14 Jun 2021Reviewer(s) Assigned
26 Sep 2021Review(s) Completed, Editorial Evaluation Pending
27 Sep 2021Editorial Decision: Revise Major
26 Jan 20221st Revision Received
27 Jan 2022Assigned to Editor
27 Jan 2022Submission Checks Completed
27 Jan 2022Reviewer(s) Assigned
08 May 2022Review(s) Completed, Editorial Evaluation Pending
09 May 2022Editorial Decision: Revise Major
07 Aug 20222nd Revision Received
09 Aug 2022Submission Checks Completed
09 Aug 2022Assigned to Editor
09 Aug 2022Reviewer(s) Assigned
27 Oct 2022Review(s) Completed, Editorial Evaluation Pending
28 Oct 2022Editorial Decision: Accept