Skip to main content
SpringerLink
Log in

Weak approximation of CKLS and CEV processes by discrete random variables

  • Published:
Lithuanian Mathematical Journal Aims and scope Submit manuscript

Abstract

In this paper, we extend to CKLS and CEV processes a known result on weak approximation of CIR processes by discrete random variables. Namely, for CKLS and CEV processes, we construct first-order split-step weak approximations that use generation of two-valued random variables at each discretization step. The accuracy of constructed approximations is illustrated by several simulation examples.

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. A. Alfonsi, On the discretization schemes for the CIR (and Bessel squared) processes, Monte Carlo Methods Appl., 11(4):355–384, 2005.

    Article  MathSciNet  Google Scholar 

  2. A. Alfonsi, High order discretization schemes for the CIR process: Application to affine term structure and Heston models, Math. Comput., 79(269):209–237, 2010.

    Article  MathSciNet  Google Scholar 

  3. K.C. Chan, G.A. Karolyi, F.A. Longstaff, and A.B. Sanders, An empirical comparison of alternative models of the short-term interest rate, J. Finance, 47:1209–1227, 1992.

    Article  Google Scholar 

  4. J.C. Cox, Notes on option pricing I: Constant elasticity of variance diffusions, The Journal of Portfolio Management, 23:15–17, 1996.

    Article  Google Scholar 

  5. J.C. Cox, J.E. Ingersoll, and S.A. Ross, A theory of the term structure of interest rates, Econometrica, 53:385–407, 1985.

    Article  MathSciNet  Google Scholar 

  6. D. Lamberton and B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall, London, 1996.

    MATH  Google Scholar 

  7. V. Mackevičius, On approximation of CIR equation with high volatility, Math. Comput. Simul., 80(5):959–970, 2010.

    Article  MathSciNet  Google Scholar 

  8. V. Mackevičius, Weak approximation of CIR equation by discrete random variables, Lith. Math. J., 51(3):385–401, 2011.

    Article  MathSciNet  Google Scholar 

  9. V. Mackevičius and G. Mongirdaitė, On backward Kolmogorov equation related to CIR process, Mod. Stoch., Theory Appl., 5(1):113–127, 2018.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225, Vilnius, Lithuania

    Gytenis Lileika & Vigirdas Mackevičius

Authors
  1. Gytenis Lileika
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vigirdas Mackevičius
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gytenis Lileika.

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

Lileika, G., Mackevičius, V. Weak approximation of CKLS and CEV processes by discrete random variables. Lith Math J 60, 208–224 (2020). https://doi.org/10.1007/s10986-020-09474-w

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10986-020-09474-w

Keywords

MSC

Search

Navigation