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Optimal system of Lie group invariant solutions for the Asian option PDE

Caister, NC and Govinder, KS and O'Hara, JG (2011) 'Optimal system of Lie group invariant solutions for the Asian option PDE.' Mathematical Methods in the Applied Sciences, 34 (11). pp. 1353-1365. ISSN 0170-4214

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Asian options are useful financial products as they guard against large price manipulations near the termination date of the contract. In addition, they are often cheaper than their vanilla European counterparts. Previous analyses of the Asian option partial differential equation (PDE) have obtained analytical solutions for the fixed strike (arithmetically averaged) Asian option (and then only with certain assumptions on the boundary conditions). Using Lie symmetry analysis we obtain an optimal system of Lie point symmetries and demonstrate that many (usually ad hoc) reductions of the Asian option PDE are contained in this minimal set. We analyse each reduction member and the feasibility of its resulting invariant solution with the boundary conditions. We show that the numerical simulations on a reduced equation are more efficient than on the original specified problem. In addition, we have found new analytical solutions in terms of Fourier transforms for the floating strike Asian option as well as the fixed strike Asian option without the simplification of the domain. Copyright © 2011 John Wiley & Sons, Ltd.

Item Type: Article
Uncontrolled Keywords: Asian option; optimal system; Lie symmetries; invariant group solutions; Monte Carlo
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 01 Feb 2013 15:13
Last Modified: 18 Aug 2022 11:03

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