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Price Deviations of S&P 500 Index Options from the Black-Scholes Formula Follow a Simple Pattern

Li, Minqiang (2008): Price Deviations of S&P 500 Index Options from the Black-Scholes Formula Follow a Simple Pattern.

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Abstract

It is known that actual option prices deviate from the Black-Scholes formula using the same volatility for different strikes. For the S&P 500 index options, we find that these deviations follow a stable pattern and are described by a simple function of at-the-money-forward total volatility. This im plies that the term structure of at-the-money-forward volatilities is su±cient to determine the entire volatility surface. We also find that the implied risk-neutral density is bimodal. The patterns we find are useful in predicting future implied volatilities.

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