Log-returns of stocks and q-Gaussian distributions : an application to risk assessment

Abstract

We propose a method to assess the risk of ?nancial time series with an unconditional distribution estimated from them. Because it is not easy to infer its tail shape due to a lack of data in a practical manner, we adapt a parametric method with a q-Gaussian distribution. We introduce Value-at-Risk (VaR) to measure risk and compare it with variance under the q-Gaussian assumption. We examine performance of the maximum likelihood estimator with the q-Gaussian log-likelihood function. By using the distribution estimates, we compute the errors, de?ned as the di?erence between estimation and the real value. Finally,we conduct an empirical analysis on log-returns of a stock traded in the Tokyo Stock Exchange by using the proposed method.