Skip to main content
Log in

Second-order IMEX scheme for a system of partial integro-differential equations from Asian option pricing under regime-switching jump-diffusion models

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

This paper studies an implicit-explicit (IMEX) finite difference scheme for solving a system of moving boundary partial integro-differential equations (PIDEs) which arises in Asian option pricing under regime-switching jump-diffusion models. First, the moving boundary PIDEs are recast into a fixed boundary problem of the PIDEs. Then the IMEX scheme is proposed to solve the problem and the second-order convergence rates are proved. Numerical examples are carried out to validate 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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Boyle, P., Draviam, T.: Pricing exotic options under regime switching. Insurance: Mathematics and Economics 40, 267–282 (2007)

    MathSciNet  MATH  Google Scholar 

  2. Roul, P.: A fourth order numerical method based on B-spline functions for pricing Asian options. Comput. Math. Appl. 80, 504–521 (2020)

    Article  MathSciNet  Google Scholar 

  3. Chen, Y. Z., Xiao, A. G., Wang, W. S.: An IMEX-BDF2 compact scheme for pricing options under regime-switching jump-diffusion models. Math. Methods Appl. Sci. 42, 2646–2663 (2019)

    Article  MathSciNet  Google Scholar 

  4. Dubois, F., Lelièvre, T.: Efficient pricing of Asian options by the PDE approach. J. Comput. Finance 8, 55–64 (2005)

    Article  Google Scholar 

  5. Dang, D. M., Nguyen, D., Sewell, G.: Numerical schemes for pricing Asian options under state-dependent regime-switching jump-diffusion models. Comput. Math. Appl. 71, 443–458 (2016)

    Article  MathSciNet  Google Scholar 

  6. Kwon, Y., Lee, Y.: A second-order finite difference method for option pricing under jump-diffusion models. SIAM J. Numer. Anal. 49, 2598–2617 (2011)

    Article  MathSciNet  Google Scholar 

  7. Lee, Y. H.: Financial options pricing with regime-switching jump-diffusions. Comput. Math. Appl. 68, 392–404 (2014)

    Article  MathSciNet  Google Scholar 

  8. Kadalbajoo, M. K., Tripathi, L. P., Kumar, K.: Second order accurate IMEX methods for option pricing under Merton and Kou jump-diffusion model. J. Sci. Comput. 65, 979–1024 (2015)

    Article  MathSciNet  Google Scholar 

  9. Kadalbajoo, M. K., Tripathi, L. P., Kumar, K.: An error analysis of a finite element method with IMEX-time semidiscretizations for some partial integro-differential inequalities arising in the pricing of American options. SIAM J. Numer. Anal. 55, 869–891 (2017)

    Article  MathSciNet  Google Scholar 

  10. Kazmi, K.: An IMEX predictor-corrector method for pricing options under regime-switching jump-diffusion models. Int. J. Comput. Math. 96, 1137–1157 (2019)

    Article  MathSciNet  Google Scholar 

  11. Ma, J. T., Zhou, Z.: Convergence rates of moving mesh Rannacher methods for PDEs of Asian options pricing. J. Comput. Math. 34, 265–286 (2016)

    Article  MathSciNet  Google Scholar 

  12. Ma, J. T., Zhou, Z.: Moving mesh methods for pricing Asian options with regime switching. J. Comput. Appl. Math. 298, 211–221 (2016)

    Article  MathSciNet  Google Scholar 

  13. Ma, J. T., Wang, H.: Convergence rates of moving mesh methods for moving boundary partial integro-differential equations from regime-switching jump-diffusion Asian option pricing. J. Comput. Appl. Math. 370, 1–16 (2020)

    MathSciNet  MATH  Google Scholar 

  14. Morton, K. W., Mayers, D. F.: Numerical Solution of Partial Differential Equations. Cambridge University Press, UK (2005)

    Book  Google Scholar 

  15. Salmi, S., Toivanen, J.: IMEX schemes for pricing options under jump-diffusion models. Appl. Numer. Math. 84, 33–45 (2014)

    Article  MathSciNet  Google Scholar 

  16. Salmi, S., Toivanen, J., Von Sydow, L.: An IMEX-scheme for pricing options under stochastic volatility models with jumps. SIAM J. Sci. Comput. 36, B817–B834 (2014)

    Article  MathSciNet  Google Scholar 

  17. Večeř, J.: A new PDE approach for pricing arithmetic average Asian options. J. Comput. Finance 4, 105–113 (2001)

    Article  Google Scholar 

  18. Wang, W., Chen, Y., Fang, H.: On the vatiable two-step IMEX BDF methods for parabolic integro-differential equations with nonsmooth initial data arising in finance. SIAM J. Numer. Anal. 57, 1289–1317 (2019)

    Article  MathSciNet  Google Scholar 

  19. Sydow, L. V., Toivanen, J., Zhang, C.: Adaptive finite difference and IMEX time-stepping to price options under Bates model. Int. J. Comput. Math. 92, 2515–2529 (2015)

    Article  MathSciNet  Google Scholar 

  20. Zvan, R., Forsyth, P. A., Vetzal, K. R.: Robust numerical methods for PDE models of Asian options. J. Comput. Finance 1, 39–78 (1998)

    Article  Google Scholar 

Download references

Acknowledgements

The author is grateful to the anonymous referees for their valuable comments that have led to a greatly improved paper.

Funding

The work was supported by the Technology and Venture Finance Research Center of Sichuan Key Research Base for Social Sciences (Grant No. KJJR2019-003).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yong Chen.

Ethics declarations

The author declares that there are no in the following cases: conflicts of interest, research involving human participants and/or animals, informed consent.

Additional information

Publisher’s note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, Y. Second-order IMEX scheme for a system of partial integro-differential equations from Asian option pricing under regime-switching jump-diffusion models. Numer Algor 89, 1823–1843 (2022). https://doi.org/10.1007/s11075-021-01174-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-021-01174-x

Keywords

Mathematics Subject Classification (2010)

Navigation