Continuously Monitored Barrier Options Under Markov Processes

38 Pages Posted: 10 Jan 2013

Multiple version iconThere are 2 versions of this paper

Date Written: January 2013

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

Suggested Citation

Mijatovic, Aleksandar and Pistorius, Martijn, Continuously Monitored Barrier Options Under Markov Processes (January 2013). Mathematical Finance, Vol. 23, Issue 1, pp. 1-38, 2013, Available at SSRN: https://ssrn.com/abstract=2198772 or http://dx.doi.org/10.1111/j.1467-9965.2011.00486.x

Aleksandar Mijatovic (Contact Author)

Imperial College London ( email )

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

HOME PAGE: http://www3.imperial.ac.uk/people/a.mijatovic

Martijn Pistorius

Imperial College London ( email )

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

HOME PAGE: http://www3.imperial.ac.uk/people/m.pistorius

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