A Harris process to model stochastic volatility

Abstract

We present a tractable non-independent increment process which provides a high modeling flexibility. The process lies on an extension of the so-called Harris chains to continuous time being stationary and Feller. We exhibit constructions, properties, and inference methods for the process. Afterwards, we use the process to propose a stochastic volatility model with an arbitrary but fixed invariant distribution, which can be tailored to fit different applied scenarios. We study the model performance through simulation while illustrating its use in practice with empirical work. The model proves to be an interesting competitor to a number of short-range stochastic volatility models.

Nonlinear Stochastic Equation within an Itô Prescription for Modelling of Financial Market

“…Another quantity of interest in price dynamics is the return . Its statistical analysis is well known as distribution of returns: , where the long tail cumulative probabilities distribution of volatilities g obeys to an inverse cubic-law , where is the tail exponent [ 4 , 6 , 9 , 14 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ].…”