CONTINUOUSLY MONITORED BARRIER OPTIONS UNDER MARKOV PROCESSES

@article{Mijatovi2009CONTINUOUSLYMB,
  title={CONTINUOUSLY MONITORED BARRIER OPTIONS UNDER MARKOV PROCESSES},
  author={Aleksandar Mijatovi{\'c} and Martijn Pistorius},
  journal={Mathematical Finance},
  year={2009},
  volume={23}
}
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. 
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