Simulation Methods for Levy-Driven CARMA Stochastic Volatility Models

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Abstract
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.