Estimation for Non-negative, Levy-Driven Ornstein-Uhlenbeck Processes

• Activity Number: 339
• Type: Contributed
• Date/Time: Tuesday, July 31, 2007 : 2:00 PM to 3:50 PM
• Sponsor: Section on Risk Analysis
• Author(s): Yu Yang*+ and Peter J. Brockwell and Richard A. Davis
• Companies: Colorado State University and Colorado State University and Colorado State University
• Keywords: continuous-time autoregression ; Ornstein-Uhlenbeck process ; Levy process ; stochastic differential equation ; sampled process ; stochastic volatility model

Abstract

The Ornstein-Uhlenbeck process (or stationary continuous-time autoregression of order 1 (i.e., CAR(1)) driven by nondecreasing Levy process has been used to model stochastic volatility of the log prices of financial assets (e.g., Barndorff-Nielsen and Shephard (2001)). In this talk, I will present a highly efficient method of estimation for the parameters of a CAR(1), taking advantage of the non-negativity of the driving process. I will also show how to reconstruct the background driving Levy process from a continuously observed realization of the process and use this result to estimate the increments of the Levy process itself when closely-spaced observations are available. Lastly, I derive the asymptotic distribution of the coefficient estimator for a gamma-driven CAR(1) and illustrate the performance of the procedure through a simulation study.