A Functional Central Limit Theorem for the Realized Power Variation of Integrated Stable Processes

Abstract

In this article, we consider the asymptotic behavior of the realized power variation of processes of the form , where S ^α is an α-stable process with index of stability 0 < α < 2 and u is a process of finite q-variation with , which may be correlated to S ^α. We establish stable convergence of the corresponding fluctuations. These results provide statistical tools to infer the process u from discrete observations, which e.g., in the framework of mathematical finance leads to estimates of the integrated volatility in pure jump models with leverage.

Keywords:

• Central limit theorem
• p-variation
• Realized power variation
• Stable processes
• Young inequality

Mathematics Subject Classification:

• 60F05
• 60G15
• 60G18
• 62M99