American Journal of Applied Mathematics

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Efficient Pricing of European Options with Stochastic Interest Rate Using Fourier Transform Method

Received: 06 May 2016    Accepted: 20 May 2016    Published: 13 July 2016
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Abstract

The inclusion of stochastic interest rate is an essential element of any realistic option pricing method. Therefore, the purpose of this paper is to incorporate interest rates in the Fourier transform method for pricing European options in exponential Levy models. With the assumption of stochastic independence between the underlying log asset price and the stochastic interest rate, we obtain a pricing of pure discount bond available in the market. Our method of valuation is to apply eigenfunction expansion to the variable that describes the evolution of the interest rate, and Fourier transform to the variable that describes the log asset price.

DOI 10.11648/j.ajam.20160404.13
Published in American Journal of Applied Mathematics (Volume 4, Issue 4, August 2016)
Page(s) 181-185
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

Fourier Transform, Eigenfunction Expansion, Stochastic Interest Rate, Levy Process, Simple Harmonic Oscillator

References
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[17] Boyarchenko, N. and Levendorskii, S. Z. (2004). Eigenfunction Expansion method in multi-factor quadratic term-structure models. Working paper. Available at SSRN: http://ssrn.com/abstract=627642
[18] Cox, J. C., Ingersol, J. E and Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica 55, 349-383.
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[20] Gorovoi, V. and Linetsky, V. (2004) Black’s model of interest rates as options, eigenfunction expansion and Japanese interest rates. Mathematical Finance, 14 (1), 48-78.
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Author Information
  • Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria

  • Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria

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    Michael Chimezie Anyanwu, Roseline Ngozi Okereke. (2016). Efficient Pricing of European Options with Stochastic Interest Rate Using Fourier Transform Method. American Journal of Applied Mathematics, 4(4), 181-185. https://doi.org/10.11648/j.ajam.20160404.13

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    ACS Style

    Michael Chimezie Anyanwu; Roseline Ngozi Okereke. Efficient Pricing of European Options with Stochastic Interest Rate Using Fourier Transform Method. Am. J. Appl. Math. 2016, 4(4), 181-185. doi: 10.11648/j.ajam.20160404.13

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    AMA Style

    Michael Chimezie Anyanwu, Roseline Ngozi Okereke. Efficient Pricing of European Options with Stochastic Interest Rate Using Fourier Transform Method. Am J Appl Math. 2016;4(4):181-185. doi: 10.11648/j.ajam.20160404.13

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  • @article{10.11648/j.ajam.20160404.13,
      author = {Michael Chimezie Anyanwu and Roseline Ngozi Okereke},
      title = {Efficient Pricing of European Options with Stochastic Interest Rate Using Fourier Transform Method},
      journal = {American Journal of Applied Mathematics},
      volume = {4},
      number = {4},
      pages = {181-185},
      doi = {10.11648/j.ajam.20160404.13},
      url = {https://doi.org/10.11648/j.ajam.20160404.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.20160404.13},
      abstract = {The inclusion of stochastic interest rate is an essential element of any realistic option pricing method. Therefore, the purpose of this paper is to incorporate interest rates in the Fourier transform method for pricing European options in exponential Levy models. With the assumption of stochastic independence between the underlying log asset price and the stochastic interest rate, we obtain a pricing of pure discount bond available in the market. Our method of valuation is to apply eigenfunction expansion to the variable that describes the evolution of the interest rate, and Fourier transform to the variable that describes the log asset price.},
     year = {2016}
    }
    

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    T1  - Efficient Pricing of European Options with Stochastic Interest Rate Using Fourier Transform Method
    AU  - Michael Chimezie Anyanwu
    AU  - Roseline Ngozi Okereke
    Y1  - 2016/07/13
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    AB  - The inclusion of stochastic interest rate is an essential element of any realistic option pricing method. Therefore, the purpose of this paper is to incorporate interest rates in the Fourier transform method for pricing European options in exponential Levy models. With the assumption of stochastic independence between the underlying log asset price and the stochastic interest rate, we obtain a pricing of pure discount bond available in the market. Our method of valuation is to apply eigenfunction expansion to the variable that describes the evolution of the interest rate, and Fourier transform to the variable that describes the log asset price.
    VL  - 4
    IS  - 4
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