Modeling financial asset returns with shot noise processes

Abstract

We introduce a new class of continuous time processes for modeling the rate of returns of financial assets. The statistical characterization is based on the so-called shot noise processes. The probabilistic structure of the shot noise process provides a very realistic framework for asset returns modeling of the stock price processes. Our class of processes exhibits the natural phenomena well known in empirical financial studies: 1. (a) fat-tail distribution function for the asset returns, 2. (b) dependence of the returns, 3. (c) nonstationarity in time. Financial asset returns in new emerging markets such as those of Eastern European countries exhibit a highly volatile behavior. Statistical investigations of the unconditional distribution of returns of stocks, commodities, exchange rates, etc., show extremely heavy tails and steep peaks around the expectation. We use a class of shot noise processes with Poissonian times and Brownian magnitudes for modeling this phenomenon.