Skip to main content
SpringerLink
Log in

An Uncertain Exponential Ornstein–Uhlenbeck Interest Rate Model with Uncertain CIR Volatility

  • Original Paper
  • Published:
Bulletin of the Iranian Mathematical Society Aims and scope Submit manuscript

Abstract

Assuming that the volatility process follows the uncertain Cox–Ingersoll–Ross (CIR) model, this paper presents a new version of the uncertain exponential Ornstein–Uhlenbeck interest rate model. The prices of the interest rate ceiling and the interest rate floor based on the model are derived using the Yao–Chen formula. Some algorithms are designed to calculate the prices of these derivatives numerically. We present some numerical experiments which illustrate the behaviour of the proposed model.

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

Access this article

Log in via an institution

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. Benth, F.E., Espen, F., Rüdiger, B., Süss, A.: Ornstein–Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility. Stoch. Proc. Appl. 128, 461–486 (2018)

    Article  MathSciNet  Google Scholar 

  2. Chen, X., Gao, L.: Two-factor term structure model with uncertain volatility risk. Soft Comput. 22, 5835–5841 (2018)

    Article  Google Scholar 

  3. Chen, X., Gao, L.: Uncertain term structure model of interest rate. Soft Comput. 17, 597–604 (2013)

    Article  Google Scholar 

  4. Gao, X.: Some properties of continuous uncertain measure. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 17, 419–426 (2009)

    Article  MathSciNet  Google Scholar 

  5. Gupta, A., Subrahmanyam, M.G.: Pricing and hedging interest rate options: evidence from cap-floor markets. J. Bank. Finance 29, 701–723 (2002)

    Article  Google Scholar 

  6. Hassanzadeh, S., Mehrdoust, F.: Valuation of European option under uncertain volatility model. Soft Comput. 22, 4153–4163 (2018)

    Article  Google Scholar 

  7. Liu, B.: Some research problems in uncertainty theory. J. Uncertain. Syst. 3, 3–10 (2009)

    Google Scholar 

  8. Liu, B.: Uncertainty Theory, Studies in Fuzziness and Soft Computing. Springer, London (2007)

    Google Scholar 

  9. Liu, Y.H., Ha, M.: Expected value of function of uncertain variables. J. Uncertain. Syst. 4, 181–186 (2010)

    Google Scholar 

  10. Marcozzi, M.D.: On the valuation of interest rate products under multi factor HJM term structures. Appl. Numer. Math. 59, 2873–2890 (2009)

    Article  MathSciNet  Google Scholar 

  11. Suarez-Taboada, M., Vazquez, C.: Numerical solution of a PDE model for a ratchet-cap pricing with BGM interest rate dynamics. Appl. Math. Comput. 218, 217–5230 (2012)

    MathSciNet  MATH  Google Scholar 

  12. Sun, Y.: Interest rate model in uncertain environment based on EOU equation. Soft Comput. 22, 465–475 (2018)

    Article  Google Scholar 

  13. Sun, Y., Su, T.: Mean-reverting stock model with floating interest rate in uncertain environment. Fuzzy Optim. Decis. Mak. 16, 235–255 (2017)

    Article  MathSciNet  Google Scholar 

  14. Wang, X., Ning, Y.: An uncertain currency model with floating interest rates. Soft Comput. 21, 6739–6754 (2017)

    Article  Google Scholar 

  15. Wang, W., Chen, P.: Valuation of stock loan under uncertain stock model with floating interest rate. Soft Comput. 1–12 (2019)

  16. Yao, K.: Uncertain Differential Equation. Uncertain Differential Equations, pp. 49–94. Springer, Berlin (2016)

  17. Yao, K., Chen, X.: A numerical method for solving uncertain differential equations. J. Intell. Fuzzy Syst. 25, 825–832 (2013)

    Article  MathSciNet  Google Scholar 

  18. Yao, K.: Extreme values and integral of solution of uncertain differential equation. J. Uncertain. Anal. Appl. 1 (2013)

  19. You, C.: Some convergence theorems of uncertain sequences. Math. Comput. Model. 49, 482–487 (2009)

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the Editor and the anonymous referee for their valuable suggestions that improved the presentation of the paper.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran

    Farshid Mehrdoust & Ali Reza Najafi

Authors
  1. Farshid Mehrdoust
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Reza Najafi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Farshid Mehrdoust.

Additional information

Communicated by Hamid Reza Ebrahimi Vishki.

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

Mehrdoust, F., Najafi, A.R. An Uncertain Exponential Ornstein–Uhlenbeck Interest Rate Model with Uncertain CIR Volatility. Bull. Iran. Math. Soc. 46, 1405–1420 (2020). https://doi.org/10.1007/s41980-019-00332-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41980-019-00332-1

Keywords

Mathematics Subject Classification

Search

Navigation