An Eulerian-Lagrangian method for option pricing in finance

This article is devoted to the development and application of an Eulerian-Lagrangian method (ELM) for the solution of the Black-Scholes partial differential equation for the valuation of European option contracts. This method fully utilizes the transient behavior of the governing equations and generates very accurate option's fair values and their derivatives also known as option Greeks, even if coarse spatial grids and large time steps are used. Numerical experiments on two standard option contracts are presented which show that the ELM method (favorably) compares in terms of accuracy and efficiency to many other well-perceived methods.