Stochastic Volatility as a Simple Generator of Financial Power-Laws and Long Memory

Abstract

There has been renewed interest in power-laws and various types of self-similarity in many financial time series. Most of these tests are visual in nature, and do not consider a wide range of possible candidate stochastic models capable of generating the observed results. This paper presents a relatively simple stochastic volatility model which is able to display power laws and scale invariance similar to actual financial data even though it is constructed to have none of these properties. The primary mechanism is that volatility is assumed to have a driving process with a half life that is long relative to the tested aggregation ranges. It is argued that this might be a reasonable feature for financial, and other macroeconomic time series.

Keywords: Volatility, Power-laws, Long Memory

JEL Classification: G12, C22