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Multilevel Path Simulation for Jump-Diffusion SDEs

  • Yuan Xia
  • Michael B. Giles
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 23)

Abstract

We investigate the extension of the multilevel Monte Carlo path simulation method to jump-diffusion SDEs. We consider models with finite rate activity using a jump-adapted discretisation in which the jump times are computed and added to the standard uniform discretisation times. The key component in multilevel analysis is the calculation of an expected payoff difference between a coarse path simulation and a fine path simulation with twice as many timesteps. If the Poisson jump rate is constant, the jump times are the same on both paths and the multilevel extension is relatively straightforward, but the implementation is more complex in the case of state-dependent jump rates for which the jump times naturally differ.

Keywords

Jump Rate Barrier Option Jump Time Multilevel Method European Call Option 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Xia is grateful to the China Scholarship Council for financial support, and the research has also been supported by the Oxford-Man Institute of Quantitative Finance. The authors are indebted to two anonymous reviewers for their invaluable comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Oxford-Man Institute of Quantitative FinanceOxfordUK

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