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Biometrika Advance Access originally published online on August 5, 2007
Biometrika 2007 94(3):627-646; doi:10.1093/biomet/asm048
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Copyright © 2007 Biometrika Trust

Articles

Simulation and inference for stochastic volatility models driven by Lévy processes

Matthew P. S. Gander

Department of Mathematics, Imperial College London, London, SW7 2AZ, U.K.

David A. Stephens

Department of Mathematics and Statistics, McGill University, H3A 2KG, Montreal, Canada

m.gander{at}imperial.ac.uk

d.stephens{at}math.mcgill.ca

Received for publication 1 February 2005. Revision received 1 December 2006.
  Abstract

We study Ornstein-Uhlenbeck stochastic processes driven by Lévy processes, and extend them to more general non-Ornstein-Uhlenbeck models. In particular, we investigate the means of making the correlation structure in the volatility process more flexible. For one model, we implement a method for introducing quasi long-memory into the volatility model. We demonstrate that the models can be fitted to real share price returns data.


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