Crash–O–Phobia

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Abstract
From a large options data set on major equity indexes across the world, the authors find that worldwide, implied volatilities of options on equity indexes exhibit strikingly similar behaviors. When plotted against moneyness, implied volatilities show a heavily skewed smirk pattern, implying that out–of–the–money put options are more expensive than the corresponding out–of–the–money call options and that the risk–neutral return distribution for these indexes is heavily negatively skewed. Furthermore, as the option maturity increases from one month to five years, the implied volatility smirk does not flatten out but steepens, indicating that the risk–neutral distribution of equity index returns becomes even more negatively skewed at longer horizons. The average term structure of the implied volatility level is relatively flat, and the standard deviation of the implied volatility declines as maturity increases. Although fairly persistent, the implied volatility series are stationary. Finally, principal compo...