Volatility smile

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Volatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter (implied volatility) that needs to be modified for the Black–Scholes formula to fit market prices. Generally, for a given expiration, options whose strike price differs substantially from the underlying asset's forward price tend to have prices that deviate from their expected prices using a constant-volatility model based on the at-the-money (strike price near the underlying's forward price). Graphing implied volatilities against strike prices for a given expiry produces a skewed "smile" instead of the expected flat surface. The pattern differs across various markets. Equity options traded in American markets did not show a significant volatility smile before the Crash of 1987 but began showing one afterwards. It is believed that investor reassessments of the probabilities of fat-tail have led to higher prices for out-of-the-money options. This anomaly implies deficiencies in the...

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