Precificação de opções financeiras : um estudo sobre os modelos de Black Scholes e Garch

Abstract

This study analyzes the theoretical and empirical properties of three models for pricing options on financial stocks: Black Scholes (1973), ad-hoc Black Scholes (Dumas, Fleming and Whaley, 1998), and the asymmetric GARCH model proposed by Heston and Nandi (2000), or HN-GARCH. The models are tested in call s options on shares of Petrobras. It is shown that the Black Scholes model (1973), by assuming that the variance of the underlying asset is constant, showed the worst performance prediction compared to the other two models that consider volatility a variable. While the model adhoc Black Scholes priced much better options deep in the money, in the money and deep out of the money, the HN-GARCH model had superior performance for at the money and out of the money options.