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. DOI https://doi.org/10.1016/j.cam.2011.03.009
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. DOI https://doi.org/10.1016/j.cam.2011.03.009
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. DOI https://doi.org/10.1016/j.cam.2011.03.009
Abstract
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 |
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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 > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 01 Feb 2013 16:01 |
Last Modified: | 30 Oct 2024 19:53 |
URI: | http://repository.essex.ac.uk/id/eprint/5440 |