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Smoothing the Volatility Smile using the Corrado-Su Model

Última alteração: 2014-09-05

#### Resumo

The expansion of the derivatives market both globally and particularly in Brazil has driven users to enhance and develop tools for more efficient pricing. However, despite this expansion of the derivatives market, certain characteristics of the Brazilian options market still impose limits on its analysis and thus the studies performed. Despite the most commonly used pricing model in Brazil being that of the Black-Scholes, its assumption of constant asset’s volatility up to maturity and log-normal distribution price are criticized by a number of authors, because those are not sustained in real-life situations and consequently leads to inconsistencies. The objective of the model suggested by Corrado and Su, and improved by Brown and Robinson, is to adapt the BS model to the distribution of the asset intended for pricing by introducing the returns’ kurtosis and skewness. For this reason, it is expected that the model will be more apt for calculating implied volatility in order to reduce the volatility smile. The purpose of this paper is to show which window of observation generates the kurtosis and skewness which smoothes the volatility smile most, using the Corrado-Su model. Therefore, the companies chosen for the study were Petrobrás PN and Vale PNA, because their stocks and options are the most liquid on the Brazilian market. The data analysis indicated a smoother volatility smile using short term observation windows rather than long term windows and a performance of earlier windows equivalent to those of the Black-Scholes model.

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