Skip to main content
Log in

Pricing American put option under fractional Heston model

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

In this paper, we attempt to provide a solution for the fractional linear complementarity problem related to the evaluation of American put option generated by the fractional Heston stochastic volatility model. Using the Adomian decomposition, a numerical investigation is conducted to confirm the theoretical results.

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
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. A Bensoussan, Acta Appl. Math. 2, 139 (1984)

    MathSciNet  Google Scholar 

  2. N El Karoui, C Kapoudjan, E Pardoux, S Peng and M C Quenez, Ann. Probab. 25, 702 (1997)

    Article  MathSciNet  Google Scholar 

  3. I Karatzas, Appl. Math. Opt. 17, 37 (1988)

    Article  Google Scholar 

  4. F A Longstaff and E S Schwartz, Rev. Financ. Stud. 14, 113 (2001)

    Article  Google Scholar 

  5. F Black and M S Scholes, J. Polit. Econ. 81, 637 (1973)

    Article  MathSciNet  Google Scholar 

  6. S L Heston, Rev. Financ. Stud. 6, 327 (1993)

    Article  MathSciNet  Google Scholar 

  7. J Detemple and W Tian, Manage. Sci. 48, 917 (2002)

  8. J Huang, M Subrahmanyam and G Yu, Rev. Financ. Stud. 9, 277 (1996)

  9. I J Kim, Rev. Financ. Stud. 3, 547 (1990)

  10. M Broadie and P Glasserman, J. Econ. Dyn. Control. 21, 1267 (1997)

  11. L Rogers, Math. Financ. 12, 271 (2002)

    Article  Google Scholar 

  12. V Bally, L Caramellino and A Zanette, R-4804, INRIA. 2003. inria-00071782 (2005)

  13. M Kharrat, Rev. Union. Mat. Argent. 60, 137 (2019)

    Article  MathSciNet  Google Scholar 

  14. LA Turki and B Lapeyre, SIAM J. Finan. Math. 3, 479 (2012)

    Article  Google Scholar 

  15. M Brennan and ES Schwartz, https://doi.org/10.1111/j.1540-6261.1977.tb03284.x (1977)

  16. S Ikonen and J Toivanen, Numer. Meth. Part. D E 24, 104 (2007)

    Article  Google Scholar 

  17. D Kumar, J Singh and D Baleanu, Appl. Sci. 43(1), 443 (2019)

    Google Scholar 

  18. D Kumar, J Singh, K Tanwar and D Baleanu, Int. J. Heat Mass Transfer 138, 1222 (2019).

    Article  Google Scholar 

  19. G Amit, J Singh, D Kumar and Sushila, Physica A 524, 563 (2019)

  20. H M Srivastava, V P Dubey, R Kumar, J Singh, D Kumar and D Baleanu, Chaos Solitions Fractals 138, 109880 (2020)

    Article  Google Scholar 

  21. P Veeresha, D G Prakasha, D Kumar, D Baleanu and J Singh, J. Comput. Nonlin. Dyn. 15, 071003 (2020)

    Article  Google Scholar 

  22. H A Fallahgoul, S M Focardi and F J Fabozzi, Fractional partial differential equation and option pricing, fractional calculus and fractional processes with applications to financial economics theory and application (Elsevier, London, UK, 2017)

  23. M A M Ghandehari and M Ranjbar, Int. J. Nonlinear Sci. 17, 105 (2014)

    MathSciNet  Google Scholar 

  24. M A M Ghandehari and M Ranjbar, Comput. Meth. Diff. Equs 2, 1 (2014)

  25. S Kumar, A Yildirim, Y Khan, H Jafari, K Sayevand and L Wei, J. Frac. Calc. Appl. 2, 1 (2012)

    Google Scholar 

  26. M Kharrat, Nonlinear Dynam. Syst. Theory 18, 191 (2018)

    Google Scholar 

  27. Y Xiaozhong, W Lifei, S Shuzhen and Z Xue, Adv. Differ. Equ-Ny. 1, 1 (2016)

  28. H Zhang, F Liub, I Turner and Q Yang, Comput. Math. Appl. 71, 1772 (2016)

    Article  MathSciNet  Google Scholar 

  29. Z Zhou and X Gao, Math. Probl. Eng. 2016, Article ID 5614950 (2016)

  30. M Benchohra, J R Graef and F Z Mostefai, Nonlinear Dynam. Syst. Theory 11(3), 227 (2011)

    Google Scholar 

  31. J M Yu, Y W Luo, S B Zhou and X R Lin, Nonlinear Dynam. Syst. Theory 2, 113 (2011)

    Google Scholar 

  32. G Adomian, Nonlinear stochastic operator equations (Academic Press, New York, 1986)

    MATH  Google Scholar 

  33. V Daftardar-Gejji and S Bhalekar, Appl. Math. Comput. 202, 113 (2008)

    MathSciNet  Google Scholar 

  34. V Daftardar-Gejji and H Jafari, J. Math. Anal. Appl. 301, 508 (2005)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

Download references

Acknowledgements

The author would like to thank the referee for the constructive comments, which improved the quality and readability of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kharrat Mohamed.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mohamed, K. Pricing American put option under fractional Heston model. Pramana - J Phys 95, 3 (2021). https://doi.org/10.1007/s12043-020-02039-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-020-02039-z

Keywords

PACS Nos

Navigation