Lie symmetry, exact solutions and conservation laws of time fractional Black–Scholes equation derived by the fractional Brownian motion
Jicheng Yu
Abstract
Abstract The Black–Scholes equation is an important analytical tool for option pricing in finance. This paper discusses the Lie symmetry analysis of the time fractional Black–Scholes equation derived by the fractional Brownian motion. Some exact solutions are obtained, the figures of which are presented to illustrate the characteristics with different values of the parameters. In addition, a new conservation theorem and a generalization of the Noether operators are developed to construct the conservation laws for the time fractional Black–Scholes equation.
Topics & Concepts
Noether's theoremMathematicsConservation lawFractional Brownian motionGeneralizationSymmetry (geometry)Black–Scholes modelFractional calculusMathematical physicsMathematical analysisApplied mathematicsBrownian motionGeometryEconometricsStatisticsVolatility (finance)LagrangianFractional Differential Equations SolutionsNonlinear Waves and SolitonsStochastic processes and financial applications