Well-balanced Levy Driven Ornstein-Uhlenbeck Processes

TL;DR

This paper introduces a new well-balanced Levy-driven Ornstein-Uhlenbeck process with continuous paths and flexible autocorrelation, useful for modeling mean or volatility in stochastic processes.

Contribution

The paper presents a novel well-balanced Levy-driven Ornstein-Uhlenbeck process with unique autocorrelation properties and continuous sample paths, expanding modeling options.

Findings

Process has continuous sample paths

Autocorrelation decreases as λ|u|exp(-λ|u|)

Allows for positive and negative correlation of increments

Abstract

In this paper we introduce the well-balanced L\'{e}vy driven Ornstein-Uhlenbeck process as a moving average process of the form $X_t=\int \exp(-\lambda |t-u|)dL_u$. In contrast to L\'{e}vy driven Ornstein-Uhlenbeck processes the well-balanced form possesses continuous sample paths and an autocorrelation function which is decreasing not purely exponential but of the order $\lambda |u|\exp(-\lambda |u|)$. Furthermore, depending on the size of $\lambda$ it allows both for positive and negative correlation of increments. We indicate how the well-balanced Ornstein-Uhlenbeck process might be used as mean or volatility process in stochastic volatility models.