On the Solution of Fractional Option Pricing Model by Convolution Theorem

  • A. I. Chukwunezu Department of Mathematics and Statistics, Federal Polytechnic, Nekede, Owerri, Nigeria
  • B. O. Osu Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria
  • C. Olunkwa Department of Mathematics, Abia State University, Uturu, Nigeria
  • C. N. Obi Department of Mathematics, Federal University of Technology, Owerri, Nigeria
DOI: https://doi.org/10.34198/ejms.2119.143157
Keywords: FBM, option pricing, Fourier transform, convolution theorem

Abstract

The classical Black-Scholes equation driven by Brownian motion has no memory, therefore it is proper to replace the Brownian motion with fractional Brownian motion (FBM) which has long-memory due to the presence of the Hurst exponent. In this paper, the option pricing equation modeled by fractional Brownian motion is obtained. It is further reduced to a one-dimensional heat equation using Fourier transform and then a solution is obtained by applying the convolution theorem.

Published
2019-05-07
How to Cite
Chukwunezu, A. I., Osu, B. O., Olunkwa, C., & Obi, C. N. (2019). On the Solution of Fractional Option Pricing Model by Convolution Theorem. Earthline Journal of Mathematical Sciences, 2(1), 143-157. https://doi.org/10.34198/ejms.2119.143157
Issue
Vol 2 No 1 (2019)
Section
Articles


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