Computations for the Delta Hedging of European Options by Mixed Finite Element Methods

Abstract

Mixed finite element method is applied with Crank-Nicolson method to numerical computations of Black-Scholes partial differential equation of European call options. The Lowest degree of Raviart-Thomas-Nedelec finite element space is used on one dimensional variable. By computing numerical approximations, we report superconvergence of pointwise error on Gaussian points for the derivative of the solution which is called the delta hedging as well as the solution called the option price. Also by comparing the market price and the delta hedging of the KOSPI 200 index option with the option value and the delta value, respectively, estimated by the proposed method, the accuracy of the numerical approximation of real market data is shown.