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Symmetry analysis of a model of stochastic volatility with time-dependent parameters

Sophocleous, C and O’Hara, JG and Leach, PGL (2011) 'Symmetry analysis of a model of stochastic volatility with time-dependent parameters.' Journal of Computational and Applied Mathematics, 235 (14). pp. 4158-4164. ISSN 0377-0427

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We provide the solutions for the Heston model of stochastic volatility when the parameters of the model are constant and when they are functions of time. In the former case, the solution follows immediately from the determination of the Lie point symmetries of the governing 1+1 evolution partial differential equation. This is not the situation in the latter case, but we are able to infer the essential structure of the required nonlocal symmetry from that of the autonomous problem and hence can present the solution to the nonautonomous problem. As in the case of the standard BlackScholes problem the presence of time-dependent parameters is not a hindrance to the demonstration of a solution. © 2011 Elsevier B.V. All rights reserved.

Item Type: Article
Uncontrolled Keywords: Symmetries; Stochastic processes; Nonlinear evolution equations
Subjects: 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 16:01
Last Modified: 18 Aug 2022 11:03

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