African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 257

Full Length Research Paper

Calculation of a class of Gaussian integrals: Derivation of payoff at expiry for European option

Joy Ijeoma Adindu-Dick
  • Joy Ijeoma Adindu-Dick
  • Department of Mathematics, Imo State University, Owerri, Imo State, Nigeria.
  • Google Scholar

  •  Received: 22 October 2021
  •  Accepted: 29 December 2021
  •  Published: 31 March 2022


This work deals with the calculation of a class of Gaussian integral of the form  where  Completing the squares of the exponential and changing variables led to the solution  where  denotes the cumulative standard normal distribution function. An equation which corresponds to pay-off at expiry for European option was derived.

Key words: Gaussian integral, Euler-Poisson integral, multivariable calculus, Gaussian function, European option.