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Contornando os Pressupostos de Black & Scholes: Aplicação do Modelo de Precificação de Opções de Duan no Mercado Brasileiro

Gustavo Araujo (), Claudio Barbedo, Antonio Figueiredo and Eduardo Lemgruber

No 78, Working Papers Series from Central Bank of Brazil, Research Department

Abstract: The Duan Options Pricing Model is an alternative to the Black & Scholes Model (B&S), but considers the heteroskedasticity and the non-normality of the asset-returns. This study analyzes the performance and the characteristics of this model when applied to the Brazilian market, specifically on Telebrás calls, during the period of July 1995 to June 2000. For this purpose, the prices found with the model are compared with the market prices and the ones found with the B&S model. For the construction of the Duan model, a random process is selected between GARCH(1,1), EGARCH(1,1) and TARCH (1,1) in each semester. Three different ways of estimating volatility are used in the model: the implicit one of the B&S equation, the historical one, and the GARCH one. The results suggest that the differences between the prices generated by the model and by the market are less when pricing in-the-money options, when the model uses the EGARCH(1,1) process in its construction and when the implicit volatility of B&S is used. The model highly overprices the majority of the options when it uses the GARCH (1,1) in its construction and it underprices at-the-money and out-of-the-money options when the EGARCH (1,1) process is used. The in-the-money options are always overpriced, independent of the process used.

Date: 2003-10
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