Constant volatility estimation by classical and bayesian methods in a financial market: An application to Bancolombia’s preferential prices

Abstract

In this paper we propose methods, from a classical and Bayesian approach, to estimate the constant volatility of an asset when it is not appropriate to fit heteroscedastic or stochastic volatility models relative to the sample series of the asset where no large increase in volatility is observed. To test which of the proposed methods best adapts to the variability of information and forecasts, the stochastic model proposed by Paul Samuelson is used to estimate, with minimum error, the closing prices of Bancolombia's preference shares in a sample period in which no significant jumps in the evolution of their prices are observed. From the Bayesian approach, the inverse gamma, standard Levy and Jeffreys volatility distributions are assumed a priori, with the estimation of the hyperparameters proposed by the authors. The proposed methodology is compared with classical volatility estimation and the bootstrap method. From the closing prices of Bancolombia's preference shares over a period where there is no significant increase or decrease in volatility over time, the Bayesian technique with gamma inverse prior captures the most information about sample returns, while the classical volatility estimation forecasts the asset, in and out of sample, with less error. However, forecasting the asset using either Bayesian or classical techniques does not show a significant impact.