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Double-Barrier Option Pricing Under the Hyper-Exponential Jump Diffusion Model

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Operator Theory and Harmonic Analysis (OTHA 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 358))

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Abstract

This work is devoted to the study of the valuation problem for a two-barrier option where the stock price is modeled by a Lévy process whose characteristic function is rational (hyper-exponential jump diffusion (HEJD) case). In a standard way, this problem is reduced to a convolution equation on a finite interval, which is solved explicitly using the modified Wiener–Hopf method. On the basis of the obtained explicit formulas, an algorithm for calculating the price of the option under consideration is developed and numerically implemented. On the other hand, with the help of the theory of generalized Toeplitz operators, theorems are proved about the existence and uniqueness of the solution of the original convolution equation and whether it belongs to a certain natural class of functions associated with the Sobolev spaces.

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Notes

  1. 1.

    We are deeply grateful to the referees for the useful comments that helped improve the presentation of the article.

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Authors and Affiliations

  1. Department of Mathematics, CINVESTAV–IPN, Mexico City, Mexico

    S. M. Grudsky

  2. Regional Mathematical Center of the Southern Federal University, Rostov-on-Don, Russia

    S. M. Grudsky

  3. Department of Mathematics, CINVESTAV–IPN, Mexico City, Mexico

    O. A. Mendez-Lara

Authors
  1. S. M. Grudsky
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  2. O. A. Mendez-Lara
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Correspondence to S. M. Grudsky .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, Mechanic and Computer Sciences and Regional Mathematical Center, Southern Federal University, Rostov-on-Don, Russia

    Alexey N. Karapetyants

  2. Department of Higher Mathematics, Don State Technical University, Rostov-on-Don, Russia

    Igor V. Pavlov

  3. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    Albert N. Shiryaev

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Grudsky, S.M., Mendez-Lara, O.A. (2021). Double-Barrier Option Pricing Under the Hyper-Exponential Jump Diffusion Model. In: Karapetyants, A.N., Pavlov, I.V., Shiryaev, A.N. (eds) Operator Theory and Harmonic Analysis. OTHA 2020. Springer Proceedings in Mathematics & Statistics, vol 358. Springer, Cham. https://doi.org/10.1007/978-3-030-76829-4_10

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