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- This study examines a classical Black-Scholes (BC) model for stochastic volatility with Heston process from Lie symmetry perspective. In the same way the study includes a classification of point symmetries and the corresponding modified local one-parameter transformations. Lie symmetry analysis is presented for the case where the volatility is a stochastic process.Furthermore, an invariant solutions are calculated and illustrated numerically.
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- This paper analyses the model of Black–Scholes option pricing from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the Black–Scholes equation. Furthermore, corresponding determining equations were constructed and new symmetries were found. As a result, the findings of the study demon strate of the integrability of the model to present an invariant solution for the Ornstein–Uhlenbeck stochastic process.
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