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A Lie algebraic and numerical investigation of the Black-Scholes equation with Heston volatility model. (English) Zbl 1371.91180

Summary: This work deals with an extension of the Black-Scholes model for rating options with the Heston volatility model. A Lie-algebraic analysis of this equation is applied to reduce its order and compute some of its solutions. As a result of this method, a five-parameter family of solutions is obtained. Though, these solutions do not match the terminal and boundary conditions, they can be used for the validation of numerical schemes.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
35A30 Geometric theory, characteristics, transformations in context of PDEs
35K10 Second-order parabolic equations
37L20 Symmetries of infinite-dimensional dissipative dynamical systems
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