  In this paper we present an algorithm for pricing barrier options in
one-dimensional Markov models. 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 Levy process and a local volatility
jump-diffusion. We also provide a convergence proof and error estimates for
this algorithm.
