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

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  • Li, Minqiang

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.

Suggested Citation

  • Li, Minqiang, 2008. "Price Deviations of S&P 500 Index Options from the Black-Scholes Formula Follow a Simple Pattern," MPRA Paper 11530, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:11530
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    More about this item

    Keywords

    Black Scholes formula; Implied volatility skew; Stable pattern; Risk-neutral density;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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