Communications in Mathematical Finance

The Black-Scholes Equation with Variable Volatility Through the Adomian Decomposition Method

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• Abstract

  The Black-Scholes equation is a partial differential equation characterizing the price evolution of a European call option and put option on a stock. In this work, we use the Adomian Decomposition Method (ADM) for the approximation of the solution of the Black-Scholes equation and show how it can be applied to a case in which the volatility is not constant but is dependent on the price of the underlying asset. Finally, we expose a numerical example to validate the developed method.