Finite Mixture Approximation of CARMA(p,q) Models

In this paper we show how to approximate the transition density of a CARMA(p,q) model driven by a time-changed Brownian motion based on the Gauss--Laguerre quadrature. This approach allows us to introduce an estimation method that maximizes a likelihood function constructed using the approximated transition density. We also provide formulas for the futures term structures and for prices of options written on futures when the underlying follows an exponential CARMA(p,q) model.