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Solving the Asian option PDE using lie symmetry methods

Caister, NC and O'Hara, JG and Govinder, KS (2010) 'Solving the Asian option PDE using lie symmetry methods.' International Journal of Theoretical and Applied Finance, 13 (8). 1265 - 1277. ISSN 0219-0249

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Asian options incorporate the average stock price in the terminal payoff. Examination of the Asian option partial differential equation (PDE) has resulted in many equations of reduced order that in general can be mapped into each other, although this is not always shown. In the literature these reductions and mappings are typically acquired via inspection or ad hoc methods. In this paper, we evaluate the classical Lie point symmetries of the Asian option PDE. We subsequently use these symmetries with Lie's systematic and algorithmic methods to show that one can obtain the same aforementioned results. In fact we find a familiar analytical solution in terms of a Laplace transform. Thus, when coupled with their methodic virtues, the Lie techniques reduce the amount of intuition usually required when working with differential equations in finance. © 2010 World Scientific Publishing Company.

Item Type: Article
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 01 Feb 2013 15:36
Last Modified: 31 Aug 2021 21:17

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