Avaliação de opções sob consideração de volatilidades históricas, implícitas e condicionadas: o caso TELEBRÁS na BOVESPA - Bertucci, Luiz Alberto (1999)
We measured the gains expected in the pricing of options written on Telebrás PN, using models of auto repressive volatility, and having its results were compared to those generated by numeric process of historic and implied volatility. In this task, the study's dynamic took us to establish new objectives: a) to identify more efficient models to get the average of the process on the returns of Telebrás PN, which could eventually optimize the use of ARCH models; b) to identify anomalies, if any, in the market due to the influence exerted by the sensibility of options prices on the efficiency of models of conditional volatility, in order to define the conditions to reach practical results in the field of options pricing. We noticed that ARCH models reached sensible gains in projecting volatility of returns of Telebrás PN, validating its use in the field of 'event studies' (in which the movements of the variance on time would reveal the reactions and attitudes of the market). Additionally, the models of asymmetric response (EGARCH e TARCH) were seen as more suited in this task compared to those of symmetric nature (ARCH e GARCH). Nonetheless, whenever these projected variances are used to price options, the results are inferior to those generated by implied volatility, which seems to consider more properly the specificity of the options market in its aspect of sensibility of prices in situations defined as 'in or out of the money'. We have not verified any gain in terms of predictive ability by defining ARMA parameterizations to describe the process of return of Telebrás PN, which takes us to just impose regressions on a constant in order to model the mean and to obtain the residues to generate the ARCH models. In addition to that, the efficiency of market of Bovespa seems to be clear from the conclusion that the negotiations in specific days of the week do not produce anomalies on options prices. The identification of the effect called 'volatility smile' on the series of returns of Telebrás PN, took us to conclude on the presence of a progressive abandon of the premise of neutrality to risk in the Black-Scholes models, as negotiations were processed more and more 'out of the money'. As a conclusion, the premise of an unique volatility of returns of an asset, no matter how much options have been written on it, was broken. The conclusion to be taken is not favorable to the use of models of conditional volatility in options pricing in the context of Black-Scholes models. The final conclusion of the study is that the quest for options pricing in Bovespa market seems reasonably resolved with the conjunction of implied volatility and the Black-Scholes model.