International Journal of Theoretical and Applied Mathematics

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Mathematical Modeling of Investors’ Savings Plan (ISP) with Stochastic Interest Rate via Numéraire Change

Received: 31 October 2016    Accepted: 10 December 2016    Published: 07 January 2017
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Abstract

This paper focuses on Numéraire change technique for pricing financial assets with stochastic interest rate. It makes sense to introduce the notion of stochastic interest rate when dealing with long term option pricing problems rather than constant interest rate addressed in the past by most papers. We consider the application of Numéraire Change technique to pricing of Investor’s Savings Plan (ISP) with swaption between two interest rates, inflation and exchange rates of two different countries. The result shows that it is better to incorporate stochastic interest rate into long term option pricing problems and Numéraire technique is better applied if faced with several risks factors.

DOI 10.11648/j.ijtam.20170301.14
Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 1, February 2017)
Page(s) 25-29
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Numéraire Change, Stochastic Interest Rate, Investor Savings Plan (ISP)

References
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[15] AntonioMannolini, (2014), Advanced Financial Modelling, A Crash review of the Change of Measure Theory. Lecture note 4, pg 1-9.
[16] Gawie, L. R., (2007), Applications of Change of Numéraire for Option Pricing. pp. 1-60.
[17] Geman, H. E., El Karoui, and Rouchet, J., (1995), Changes of Numeraire, Changes of Probability Measure and Option Pricing, Journal of Applied Probability, pp. 443-458.
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Author Information
  • Department of Mathematics, University of Ibadan, Ibadan, Nigeria

  • Department of Physics, Adeniran Ogunsanya College of Education, Oto/Ijanikin, Nigeria

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  • APA Style

    Philip Ajibola Bankole, Adeniyi Adewopo. (2017). Mathematical Modeling of Investors’ Savings Plan (ISP) with Stochastic Interest Rate via Numéraire Change. International Journal of Theoretical and Applied Mathematics, 3(1), 25-29. https://doi.org/10.11648/j.ijtam.20170301.14

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    ACS Style

    Philip Ajibola Bankole; Adeniyi Adewopo. Mathematical Modeling of Investors’ Savings Plan (ISP) with Stochastic Interest Rate via Numéraire Change. Int. J. Theor. Appl. Math. 2017, 3(1), 25-29. doi: 10.11648/j.ijtam.20170301.14

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    AMA Style

    Philip Ajibola Bankole, Adeniyi Adewopo. Mathematical Modeling of Investors’ Savings Plan (ISP) with Stochastic Interest Rate via Numéraire Change. Int J Theor Appl Math. 2017;3(1):25-29. doi: 10.11648/j.ijtam.20170301.14

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  • @article{10.11648/j.ijtam.20170301.14,
      author = {Philip Ajibola Bankole and Adeniyi Adewopo},
      title = {Mathematical Modeling of Investors’ Savings Plan (ISP) with Stochastic Interest Rate via Numéraire Change},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {3},
      number = {1},
      pages = {25-29},
      doi = {10.11648/j.ijtam.20170301.14},
      url = {https://doi.org/10.11648/j.ijtam.20170301.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijtam.20170301.14},
      abstract = {This paper focuses on Numéraire change technique for pricing financial assets with stochastic interest rate. It makes sense to introduce the notion of stochastic interest rate when dealing with long term option pricing problems rather than constant interest rate addressed in the past by most papers. We consider the application of Numéraire Change technique to pricing of Investor’s Savings Plan (ISP) with swaption between two interest rates, inflation and exchange rates of two different countries. The result shows that it is better to incorporate stochastic interest rate into long term option pricing problems and Numéraire technique is better applied if faced with several risks factors.},
     year = {2017}
    }
    

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    T1  - Mathematical Modeling of Investors’ Savings Plan (ISP) with Stochastic Interest Rate via Numéraire Change
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    JF  - International Journal of Theoretical and Applied Mathematics
    JO  - International Journal of Theoretical and Applied Mathematics
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    UR  - https://doi.org/10.11648/j.ijtam.20170301.14
    AB  - This paper focuses on Numéraire change technique for pricing financial assets with stochastic interest rate. It makes sense to introduce the notion of stochastic interest rate when dealing with long term option pricing problems rather than constant interest rate addressed in the past by most papers. We consider the application of Numéraire Change technique to pricing of Investor’s Savings Plan (ISP) with swaption between two interest rates, inflation and exchange rates of two different countries. The result shows that it is better to incorporate stochastic interest rate into long term option pricing problems and Numéraire technique is better applied if faced with several risks factors.
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