Implementation of Finite Difference Technique for Exotic Double Barrier Options

Abstract

In this paper, we attempt to price a complex barrier option using Finite Difference (FD) techniques. The focus is to demonstrate the strength of the FD to deal with various seemingly complicated issues like jump diffusion, Early exercise in a relatively easy way and at a lower computational cost compared to the normal Monte Carlo (MC) techniques. The prices were reliable and efficiency gains are benchmarked against the results from a pure Monte Carlo simulation and other analytical values. The paper also deals with issues on implication of dividend incorporation, treatment of boundary conditions, and hedging.