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

Minqiang Li

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Black Scholes formula; Implied volatility skew; Stable pattern; Risk-neutral density (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2008
New Economics Papers: this item is included in nep-fmk
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:11530

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