Numerical solution of Black–Scholes Partial Differential Equation using Direct solution of second-order Ordinary Differential Equation with two-step hybrid Block Method of Order seven

Abstract

This paper proposes a new numerical solution of Black-Scholes Partial Differential Equation using Direct solution of second-order Ordinary Differential Equation ODE with two-step hybrid Block Method of Order seven directly. The method is developed using interpolation and collocation techniques. The use of the power series approximate solution as an interpolation polynomial and its second derivative as a collocation equation is considered in deriving the method. Properties of the method such as zero stability, order, consistency, convergence and region of absolute stability are investigated The new method is then applied to solve Black–Scholes equation after converting it to the system of second-order ordinary differential equations and the accuracy is better when compared with the existing methods in terms of error.