Estimation of the Stochastic Volatility of Oil Prices of the Mexican Basket: An Application of Boosting Monte Carlo Markov Chain Estimation

The volatility of the returns on financial assets is not a constant number over time as many valuation models, mainly derivatives, developed during the 80's, assume. The complexity of non-heteroscedasticity and the difference in results when estimated with different methodologies such as historical, implicit or stochastic calculation, make this subject too extensive a field to be covered in this work. However, stochastic volatility has been widely accepted in recent years. Monte Carlo Markov Chain (MCMC) method is explained and used to estimate the distribution of oil prices of Mexican basket as a stochastic variable. MCMC in the univariate case, supposes that we can estimate the distribution of a latent (hidden) variable through the behavior of another variable observed posteriori with the help of Bayesian inference; this method allows an efficient inference independent of the underlying process through an algorithm. The results show a correct adjustment of stochastic volatility to the behavior of the oil prices.