Análise da estrutura fatorial de mercado em opções de ações individuais e opções de índice de mercado

Abstract

Options are financial derivatives that allow its holder, upon payment of the premium, acquire some protection against market upward and downward movements. The celebrated work of Black-Scholes (1973) boosted the scientific production of mathematical models in finance aimed at predicting the behavior of stock prices and options and other derivatives. Christoffersen, Fournier and Jacobs (2013) identified a structural factor in common between prices of stock options of companies in the Dow Jones Industries index and the S & P500 index from that discovery developed a model to valuation of stock options that take into account the stochastic volatility of the market return and idiosyncratic part of the individual firms returns. The consistency of model testing led to the investigation of the applicability of this model in Brazil. Thus, we intend to answer the following question: how the factor structure Christoffersen, Fournier and Jacobs (2013) model evaluates the prices of stock options of individual firms participating in the Ibovespa index. This is a recent and few explored model, thus, the overall objective is to evaluate the performance of the market factor structure model in predicting the prices of stock options of Petrobras S.A. and Vale S.A with maturing in 30 and 60 days. Specifically aims to: raise the price of the shares and options; investigate the existence of a structural factor in common between the prices of firms' stock options and prices of stock options of the Ibovespa stock market index, estimating the prices of options maturing in 30 and 60 days and, finally, compare the prices of models with market prices. This research is characterized in relation to the objectives as exploratory, documentary when the procedures and qualitative and quantitative as its approach. The survey data were collected from April 1 to June 30, 2015. The principal component analyze did not identify the presence of factor structure in common between the prices of the options of individual firms and the market index, showing low explanatory power. As the model’s efficiency, qualitatively, it was found that this estimate could satisfied with the devaluation of the options Petrobras with maturing in 30 and 60 days and options and Vale in 30 days. Quantitatively, the model predictions underestimated the prices of options on individual firms.