On the modified arithmetic Asian option equation and its analytical solution

Zieneb Ali Elshegmani, Rokiah Rozita Ahmed, Saiful Hafizah Jaaman @ Sharman

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Solving Black-Scholes PDE of the arithmetic Asian option is outstanding problem in Mathematics, because the PDE is a degenerate partial differential equation in three dimension. Since there is no analytical solution for the arithmetic Asian option is known yet, we are thinking about modification the Black-Scholes Asian option equation. Using general stochastic differential equation we derive a modified partial differential equation for arithmetic Asian option. We provide four different modification, which some of them can be transformed to the classical Black-Scholes PDE and then to a parabolic equation with constant coefficient, which can solved analytically using means of partial differential equations.

Original languageEnglish
Pages (from-to)1217-1227
Number of pages11
JournalApplied Mathematical Sciences
Volume5
Issue number25-28
Publication statusPublished - 2011

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Asian Options
Black-Scholes
Partial differential equations
Analytical Solution
Partial differential equation
Differential equations
Parabolic Equation
Stochastic Equations
Three-dimension
Differential equation
Coefficient

Keywords

  • Arithmetic Asian option
  • Partial differential equations
  • Stochastic differential equation

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

On the modified arithmetic Asian option equation and its analytical solution. / Elshegmani, Zieneb Ali; Ahmed, Rokiah Rozita; Jaaman @ Sharman, Saiful Hafizah.

In: Applied Mathematical Sciences, Vol. 5, No. 25-28, 2011, p. 1217-1227.

Research output: Contribution to journalArticle

Elshegmani, Zieneb Ali ; Ahmed, Rokiah Rozita ; Jaaman @ Sharman, Saiful Hafizah. / On the modified arithmetic Asian option equation and its analytical solution. In: Applied Mathematical Sciences. 2011 ; Vol. 5, No. 25-28. pp. 1217-1227.
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