Why are those options smiling?
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.
Institutional Investor, Inc.
Ederington, L.H. & Guan, W. (2002). Why are those options smiling? Journal of Derivatives, 10(2), 9-34.
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