CONTINUOUSLY MONITORED BARRIER OPTIONS UNDER MARKOV PROCESSES

Abstract. 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 L\'evy process and a local volatility
jump-diffusion. We also provide a convergence proof for this algorithm.

A Matlab implementation of the algorithm in the case of CEV diffusion processes is
available here.

An extended version of the paper is available on SSRN.

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