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Zbl 1203.91285
Caister, Nicolette C.; O'Hara, John G.; Govinder, Keshlan S.
Solving the Asian option PDE using Lie symmetry methods. (English)
[J] Int. J. Theor. Appl. Finance 13, No. 8, 1265-1277 (2010). ISSN 0219-0249

Summary: 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.

MSC 2000:: *91G20
91G80

Keywords: Asian option PDE; Lie symmetries; reductions; mappings; analytical solution; inverse Laplace transform

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Zentralblatt MATH Berlin [Germany]