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I would like to know some references regarding importance sampling algorithms for variance reduction of Monte Carlo barrier options pricing.

Please could someone help me leaving some references? If you wish to give an answer explaining/giving some hints on how to approach the variance reduction problem of barrier options Monte Carlo, it would be even better.

Many thanks

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Since there is a closed form in the BS case for continuous barrier options, you probably won't find a huge amount of work on this since it's not needed. In the discrete case, I did a paper with Tang:

http://ssrn.com/abstract=1441142

Pricing and Deltas of Discretely-Monitored Barrier Options Using Stratified Sampling on the Hitting-Times to the Barrier

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I'd recommend M. Joshi and T. Leung "Using Monte Carlo simulation and importance sampling to rapidly obtain jump-diffusion prices of continuous barrier options". Though it assumes jump-diffusion process for the returns it is straightforward to obtain the scheme for a diffusion process.

Also Paul Glasserman's [book][2]

[2]: http://www.amazon.com/Financial-Engineering-Stochastic-Modelling-Probability/dp/0387004513 contains a variance reduction example for barrier options.

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