Simulation Methods for Levy-Driven Carma Stochastic Volatility Models

41 Pages Posted: 24 Aug 2005

See all articles by George Tauchen

George Tauchen

Duke University - Economics Group

Viktor Todorov


Date Written: September 15, 2004


We develop simulation schemes for the new classes of non-Gaussian pure jump Levy processes for stochastic volatility. We write the price and volatility processes as integrals against a vector Levy process, which then makes series approximation methods directly applicable. These methods entail simulation of the Levy increments and formation of weighted sums of the increments; they do not require a closed-form expression for a tail mass function nor specification of a copula function. We also present a new, and apparently quite flexible, bivariate mixture of gammas model for the driving Levy process. Within this setup, it is quite straightforward to generate simulations from a Levy-driven CARMA stochastic volatility model augmented by a pure-jump price component. Simulations reveal the wide range of different types of financial price processes that can be generated in this manner, including processes with persistent stochastic volatility, dynamic leverage, and jumps.

Keywords: Levy process, simulation, stochastic volatility, diffusions, realized variance, quadratic variation

JEL Classification: G12, C51, C52

Suggested Citation

Tauchen, George E. and Todorov, Viktor, Simulation Methods for Levy-Driven Carma Stochastic Volatility Models (September 15, 2004). Available at SSRN: or

George E. Tauchen (Contact Author)

Duke University - Economics Group ( email )

Box 90097
221 Social Sciences
Durham, NC 27708-0097
United States
919-660-1812 (Phone)
919-684-8974 (Fax)

Viktor Todorov

Independent ( email )

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