Volatility Smiles

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Equity Options when Expecting a Large Jump‣ In order to better illustrate the behavior of equity options weshall consider the following example.‣ Consider a stock at $50 that is expected, due to the comingdetermination of a currently unknown event, to changestrongly in one month. The risk-free rate is 12%‣ We can calculate the prices of 1-month European puts andcalls with different strike prices and from them find theimplied volatility. The results are,8
‣ Plotting the implied volatility against the strike-price revealsa volatility “frown”.‣ The volatility implied from an option with a strike-price of$50 will overprice an option with a strike-price that is furtherfrom being at-the-money.‣ Remember: traders use volatility smiles to allow fornon-lognormality.The volatility smile defines the relationship between theimplied volatility of an option and its strike price. <strong>Volatility</strong> Surfaces‣ Implied volatilities are frequently used to quote the prices ofoptions.9
Page 2 and 3: ‣ The differences between these t
Page 4 and 5: Empirical Results‣ We have just s
Page 6 and 7: ‣ The volatility used to price a
Page 10 and 11: ‣ The implied volatility of a Eur
Page 12 and 13: ‣ If there is a large one-day ret
Page 14: ‣ Here there is a weighting assig

Volatility Smiles

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