Inverse transform method for simulating levy processes and discrete Asian options pricing

Zisheng Chen, Liming Feng, Xiong Lin

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The simulation of a Lévy process on a discrete time grid reduces to simulating from the distribution of a Lévy increment. For a general Lévy process with no explicit transition density, it is often desirable to simulate from the characteristic function of the Lévy increment. We show that the inverse transform method, when combined with a Hilbert transform approach for computing the cdf of the Lévy increment, is reliable and efficient. The Hilbert transform representation for the cdf is easy to implement and highly accurate, with approximation errors decaying exponentially. The inverse transform method can be combined with quasi-Monte Carlo methods and variance reduction techniques to greatly increase the efficiency of the scheme. As an illustration, discrete Asian options pricing in the CGMY model is considered, where the combination of the Hilbert transform inversion of characteristic functions, quasi-Monte Carlo methods and the control variate technique proves to be very efficient.

Original languageEnglish (US)
Title of host publicationProceedings of the 2011 Winter Simulation Conference, WSC 2011
Number of pages13
StatePublished - 2011
Event2011 Winter Simulation Conference, WSC 2011 - Phoenix, AZ, United States
Duration: Dec 11 2011Dec 14 2011

Publication series

NameProceedings - Winter Simulation Conference
ISSN (Print)0891-7736


Other2011 Winter Simulation Conference, WSC 2011
Country/TerritoryUnited States
CityPhoenix, AZ

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Computer Science Applications


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