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Second-Order Weak Approximations of CKLS and CEV Processes by Discrete Random Variables

Author

Listed:
  • Gytenis Lileika

    (Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Vigirdas Mackevičius

    (Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

Abstract

In this paper, we construct second-order weak split-step approximations of the CKLS and CEV processes that use generation of a three−valued random variable at each discretization step without switching to another scheme near zero, unlike other known schemes (Alfonsi, 2010; Mackevičius, 2011). To the best of our knowledge, no second-order weak approximations for the CKLS processes were constructed before. The accuracy of constructed approximations is illustrated by several simulation examples with comparison with schemes of Alfonsi in the particular case of the CIR process and our first-order approximations of the CKLS processes (Lileika– Mackevičius, 2020).

Suggested Citation

  • Gytenis Lileika & Vigirdas Mackevičius, 2021. "Second-Order Weak Approximations of CKLS and CEV Processes by Discrete Random Variables," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1337-:d:572021
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
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    Cited by:

    1. Vigirdas Mackevičius & Gabrielė Mongirdaitė, 2022. "Weak Approximations of the Wright–Fisher Process," Mathematics, MDPI, vol. 10(1), pages 1-20, January.

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