Symmetry analysis of a model of stochastic volatility with time-dependent parameters |
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Authors: | C Sophocleous PGL Leach |
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Institution: | a Department of Mathematics and Statistics, University of Cyprus, Lefkosia 1678, Cyprusb CCFEA, University of Essex, Wivenhoe Park, CO4 3SQ, England, United Kingdomc School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001 Durban 4000, South Africa |
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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 Black-Scholes problem the presence of time-dependent parameters is not a hindrance to the demonstration of a solution. |
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Keywords: | 35C06 35K15 60G44 91G80 |
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