Continuously Monitored Barrier Options Under Markov Processes

Abstract

In this paper we present a fast and accurate algorithm for pricing barrier options in one-dimensional Markov models, including general local volatility models with jumps, L\'evy processes and L\'evy driven SDEs. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given Markov model. We illustrate the method by implementing it for a range of models, including a local L\'evy process and a local volatility jump-diffusion. Code in Matlab for one of the numerical examples is included in the paper (and is also available online). We also provide a convergence proof and error estimates for this algorithm.

Keywords: Barrier options, Markov processes

JEL Classification: G12, G13, C63