New approach to approximate calculation of the fair price option, based on Black-Scholes model

Abstract

New approach to the approximate solution of Black-Scholes task, based on a method of power series is offered. Approximate formulas for the fair price option, using approximation of a regional condition by interpolation polynomials Lagrange are received. The developed method allows receiving approximate formulas of the fair price and in case of a variable interest rate and volatility. In work the European options for purchase and for sale, and also model with dividends are considered.