Continuously Monitored Barrier Options Under Markov Processes

62 Pages Posted: 27 Aug 2009 Last revised: 11 Oct 2010

Multiple version iconThere are 2 versions of this paper

Date Written: August 27, 2009


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

Suggested Citation

Pistorius, Martijn and Mijatovic, Aleksandar, Continuously Monitored Barrier Options Under Markov Processes (August 27, 2009). Available at SSRN: or

Martijn Pistorius

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom


Aleksandar Mijatovic (Contact Author)

Imperial College London ( email )

Department of Mathematics
180 Queen's Gate
London, SW7 2AZ
United Kingdom


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