Lecture 7 – Finite difference scheme for option pricing It is a method based on the numerical resolution of the partial differential equation (PDE) of Black & Scholes. It is based on the discretization of: time; underlying stock price option price PDE of Black & Scholes It is equivalent from a mathematical point of view to a trinomial tree 1/12/2019

Finite difference – explicit method Fix the borderline condition (i.e. the final condition for t = option expiry). The equations are solved according to a backward recursive scheme starting from maturity time, getting Fi,j in term of Fi+1,j. 1/12/2019

Finite difference - convergence 1/12/2019

Finite difference – pros and cons Simple to be implemented It is possible to use acceleration methods American options can be managed Limited to low dimensional problems Ad hoc implementations are required basing on contract typology. 1/12/2019