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

Michael Chimezie Anyanwu; Roseline Ngozi Okereke

doi:doi:10.11648/j.ajam.20160404.13

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

Michael Chimezie Anyanwu, Roseline Ngozi Okereke

Published in American Journal of Applied Mathematics (Volume 4, Issue 4)

Received: 6 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.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 4)
DOI	10.11648/j.ajam.20160404.13
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), 2016. Published by Science Publishing Group

Keywords

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

References

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[12]	Itkin, A. (2005) Pricing options with VG model using FFT. arXiv: physics/0503137v1
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[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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APA Style

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://article.sciencepublishinggroup.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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TY  - JOUR
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
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160404.13
DO  - 10.11648/j.ajam.20160404.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 181
EP  - 185
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160404.13
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
ER  -

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Author Information

Michael Chimezie Anyanwu

Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria
Roseline Ngozi Okereke

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

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APA Style

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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
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
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160404.13
DO  - 10.11648/j.ajam.20160404.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 181
EP  - 185
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160404.13
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
ER  -

Copy | Download