Finite Mixture Approximation of CARMA(p,q) Models

TL;DR

This paper introduces a method to approximate the transition density of CARMA(p,q) models using Gauss-Laguerre quadrature, enabling analytical option pricing formulas and an estimation procedure based on likelihood approximation.

Contribution

It presents a novel finite mixture approximation for CARMA(p,q) models and derives analytical option pricing formulas and estimation methods.

Findings

Effective approximation of transition densities for CARMA models.

Analytical formulas for option prices under CARMA dynamics.

A new estimation procedure based on approximated likelihood.

Abstract

In this paper we show how to approximate the transition density of a CARMA(p, q) model driven by means of a time changed Brownian Motion based on the Gauss-Laguerre quadrature. We then provide an analytical formula for option prices when the log price follows a CARMA(p, q) model. We also propose an estimation procedure based on the approximated likelihood density.