Skip to main content
Log in

Stability Analysis for Pricing European Options Regarding the Interest Rate Generated by the Time Fractional Cox-Ingersoll-Ross Processes

  • Published:
Methodology and Computing in Applied Probability Aims and scope Submit manuscript

Abstract

In this paper, we introduce a new methodology for pricing European options when the interest rate is generated by the Time Fractional Cox-Ingersoll-Ross processes. A study was undertaken to corroborate the reliability, goodness of fit and stability of our approach. Certain numerical experiments were conducted so as to prove the obtained theoretical findings.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Availability of Data and Materials

Not applicable.

References

  • Amit G, Singh J, Kumar D, Sushila (2019) An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma. Physica A 524

  • Benchohra M, Graef JR, Mostefai FZ (2011) Weak solutions for boundary-value problems with nonlinear fractional differential inclusions. Nonlinear Dyn Syst Theory 3:227–237

    MathSciNet  MATH  Google Scholar 

  • Bensoussan A (1984) On the theory of option pricing. Acta Appl Math 2:139–158

    Article  MathSciNet  MATH  Google Scholar 

  • Black F, Scholes MS (1973) The pricing of options and corporate liabilities. J Polit Econ 81:279–296

    Article  MathSciNet  MATH  Google Scholar 

  • Cox JC, Ingersoll JE, Ross SA (1985) LA theory of the term structure of interest rates. Econometrica 53:385–407

    Article  MathSciNet  MATH  Google Scholar 

  • Daftardar-Gejji V, Babakhani A (2004) Analysis of a system of fractional differential equations. J Math Anal Appl 293:511–522

    Article  MathSciNet  MATH  Google Scholar 

  • Garrappa R (2013) Exponential integrators for time-fractional partial differential equations. Eur Phys J Spec Top 222:1915–1927

    Article  Google Scholar 

  • Ghandehari MAM, Ranjbar M (2014) European option pricing of fractional version of the Black-Scholes model: approach via expansion in series. Int J Nonlinear Sci 17

  • Kaczorek T (2002) Positive 1D and 2D systems, London. Springer, London, UK

    Book  MATH  Google Scholar 

  • Kharrat M (2018) Closed-form solution of European option under fractional Heston model. Nonlinear Dyn Syst Theory 18(2):191–195

    MathSciNet  MATH  Google Scholar 

  • Kharrat M (2021a) Pricing American put option under Fractional Heston Model. Pramana J Phys 95(3):2021. https://doi.org/10.1007/s12043-020-02039-z

  • Kharrat M (2021b) Pricing American put option under fractional model. Filomat 35(10)

  • Kumar D, Singh J, Baleanu D (2019) On the analysis of vibration equation involving a fractional derivative with Mittag-Leffler law. Math Method Appl Sci 43(1)

  • Podlubny I (1999) Fractional differential equations calculus. Academic Press, New York

    MATH  Google Scholar 

  • Rafael Company, Egorova VN, Jódar L, Valls FF (2020) An ETD method for American options under the Heston Model. Comput Model Eng Sci 124(2). https://doi.org/10.32604/cmes.2020.010208

  • Srivastava HM, Dubey VP, Kumar R, Singh J, Kumar D, Baleanu D (2020) An efficient computational approach for a fractional-order biological population model with carrying capacity. Chaos Solition Fract 138

  • Vasicek O (1977) An equilibrium characterization of the term structure. J Financ Econ 5(2):177–188

    Article  MATH  Google Scholar 

  • Xiaozhong Y, LifeiEmail W, Shuzhen S, Xue Z (2016) A universal difference method for time-space fractional Black-Scholes equation. Adv Differ Equ-Ny 1

  • Yu JM, Luo YW, Zhou SB, Lin XR (2011) Existence and uniqueness for nonlinear multi-variables fractional differential equations. Nonlinear Dyn Syst Theory 2:213–221

    MathSciNet  MATH  Google Scholar 

  • Zhang H, Liu F, Turner I, Yang Q (2016) Numerical solution of the time fractional Black-Scholes model governing European options. Comput Model Eng Sci 71(Issue 16): 1772–1783

Download references

Author information

Authors and Affiliations

Authors

Contributions

The author [Mohamed Kharrat] contributed only to the development and the written of this paper.

Corresponding author

Correspondence to Mohamed Kharrat.

Ethics declarations

Conflict of Interest

The author has not any conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kharrat, M. Stability Analysis for Pricing European Options Regarding the Interest Rate Generated by the Time Fractional Cox-Ingersoll-Ross Processes. Methodol Comput Appl Probab 25, 50 (2023). https://doi.org/10.1007/s11009-023-10021-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11009-023-10021-6

Keywords

Mathematics Subject Classification

Navigation