Maturity and volatility effects on smiles or dying smiling?

• Autor(a) principal: Duque, João
• Data de Publicação: 2000
• Outros Autores: Lopes, Patrícia Teixeira
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.5/23569
• topic: Options; Implied Volatility; Smile Effect

The "smile effect" is a result of an empirical observation of the options' implied volatility with the same expiration date, across different exercise prices. It describes a U-shape form showing high implied volatilities for in and out-of-the-money options and low volatility figures for at-the-money options. We can find empirical evidence of this phenomenon. The reasons suggested in the literature were stochastic volatility, traders' behaviour, transaction costs, and the effect of dividends on pricing American options. But the most recent literature seems to conclude that the sophistication of financial modelling for option pricing is not enough for removing the "smile". In this paper we used liquid equity options on 9 stocks traded on the London International Financial Futures and Options Exchange (LIFFE) between August 1990 and December 1991. We tested two different hypothesis trying to verify the existence of two different phenomena: (1) the increase of the "smile" as maturity approaches; (2) and the association between the smile and the volatility of the underlying stock. In order to estimate implied volatilities for unavailable exercise prices, we modelled the smile using cubic B-spline curves. We found empirical support for the smile intensification (the U-shape is more pronounced) as maturity approaches as well as when volatility rises. However, this increase in the curvature is asymmetric. As maturity approaches the implied volatility of out-of-the-money options tends to be higher than the implied volatility of in-the-money options and, as the volatility of the underlying increases, the implied volatility of in-the-money options tend to be higher than implied volatility of out-of-the-money options. We claim to have detected new empirical reasons for previous empirical findings where the smile was, for some authors, a symmetric smile, while for others it converts into a "wry grin" or a "reverse grin".