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Why are those options smiling?

SelectedWorks Author Profiles:

Wei Guan

Document Type


Publication Date


Date Issued

January 2002

Date Available

April 2013




The most popular explanation of the "smile" observed in Black-Scholes implied volatilities is that it is due to erroneous assumptions in the B-S model regarding tile return distribution, whether the assumption of constant volatility or the assumption of log-normal returns, that cause the calculated implied volatilities to differ from their true values. The presumption is that if the implied volatilities were calculated using a model based on correct distributional assumptions, the smile should disappear, i.e., the volatility becomes flat. There should be no profits to a trading strategy based on the B-S smile, as the options that Black-Scholes identifies as relatively over- or underpriced are in fact correctly priced. We find, however, that in the S&P 500 options market such delta-neutral strategies yield substantial pre-transaction cost profits. Actual profits are strongly correlated with the B-S model's predictions, although generally smaller. We conclude that while part of the volatility smile may be due to erroneous distributional assumptions in the B-S model, a substantial part must reflect other forces. The smile persists despite these substantial pre-transaction cost trading profits, because maintaining the trading portfolio's original low-risk profile requires frequent rebalancing that quickly eats away at profits. Although the portfolios are originally delta-neutral and either gamma- or vega-neutral, they quickly lose this neutrality.


Abstract only. Full-text article is available through licensed access provided by the publisher. Published in Journal of Derivatives, 10(2), 9-34. DOI: 10.3905/jod.2002.319193. Members of the USF System may access the full-text of the article through the authenticated link provided.




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