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 Lévy process and a local volatility jump‐diffusion. We also provide a convergence proof and error estimates for this algorithm.

Keywords: pricing algorithms, barrier options, continuous‐time Markov chain, local volatility models with jumps, Lévy processes, normal inverse Gaussian process, variance Gamma process, CGMY model, Sato processes, local Lévy processes