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Research articles

ScienceAsia 39S (2013): 67-69 |doi: 10.2306/scienceasia1513-1874.2013.39S.067

Solving an Asian option PDE via the Laplace transform

Zieneb Ali Elshegmania,*, Rokiah Rozita Ahmadb

ABSTRACT:     Solving the Black-Scholes PDE of the arithmetic Asian options is one of the most difficult problems in financial mathematics. A variety of ways ways have been proposed to address the problem. In this study, we use the PDE approach by presenting an efficient method for pricing a continuous arithmetic Asian option. Using the Laplace transform we reduce the three-dimension partial differential equation of the arithmetic Asian option into a two-dimension ordinary differential equation. Its final analytical solution is presented. We conclude that this method is applicable to all types of arithmetic Asian options.

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a School of Mathematical Sciences, Faculty of Education, University Misurata Libya, University Kebangsaan Malaysia
b School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia

* Corresponding author, E-mail: zelsheqmani@yahoo.com

Received 7 Jan 2013, Accepted 5 Apr 2013