Transforming arithmetic Asian option PDE to the parabolic equation with constant coefficients

Zieneb Ali Elshegmani, Rokiah @ Rozita Ahmad, Saiful Hafizah Jaaman @ Sharman, Roza Hazli Zakaria

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1 Citation (Scopus)

Abstract

Arithmetic Asian options are difficult to price and hedge, since at present, there is no closed-form analytical solution to price them. Transforming the PDE of the arithmetic the Asian option to a heat equation with constant coefficients is found to be difficult or impossible. Also, the numerical solution of the arithmetic Asian option PDE is not very accurate since the Asian option has low volatility level. In this paper, we analyze the value of the arithmetic Asian option with a new approach using means of partial differential equations (PDEs), and we transform the PDE to a parabolic equation with constant coefficients. It has been shown previously that the PDE of the arithmetic Asian option cannot be transformed to a heat equation with constant coefficients. We, however, approach the problem and obtain the analytical solution of the arithmetic Asian option PDE.

Original languageEnglish
Article number401547
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume2011
DOIs
Publication statusPublished - 2011

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Asian Options
Parabolic Equation
Partial differential equation
Coefficient
Heat Equation
Analytical Solution
Volatility
Closed-form
Numerical Solution
Transform

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

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AU - Jaaman @ Sharman, Saiful Hafizah

AU - Zakaria, Roza Hazli

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