FDMs and Transformation Methods for nonlinear BS equations

Abstract

Vera Egorova started her position in ITN Strike as Early-Stage-Researcher (ESR4) on September 1, 2013. The work is under the supervision of Prof. Lucas Jódar and Prof. Rafael Company. This Project is focused on numerical analysis and computing of finite difference schemes for the nonlinear Black-Scholes (BS) model. The American style option is the starting point of interest and the front-fixing method is a useful and efficient tool for the free boundary value problem associated to the American option. There exist several front-fixing transformations that are considered. A new, novel, transformation is applied to the American call option pricing problem. An analysis of properties for the numerical solutions of option pricing models as the positivity, stability and consistency of the solutions is done.