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Accouting for Biases in Black-Scholes

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Author Info

  • David Backus

    (New York University)

  • Silverio Foresi

    (Goldman Sachs)

  • Liuren Wu

    (Fordham University)

Abstract

Prices of currency options commonly differ from the Black-Scholes formula along two dimensions: implied volatilities vary by strike price (volatility smiles) and maturity (implied volatility of at­the­money options increases, on average, with maturity). We account for both using Gram­Charlier expansions to approximate the conditional distribution of the logarithm of the price of the underlying security. In this setting, volatility is approximately a quadratic function of moneyness, a result we use to infer skewness and kurtosis from volatility smiles. Evidence suggests that both kurtosis in currency prices and biases in Black­Scholes option prices decline with maturity.

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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0207008.

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Length: 41 pages
Date of creation: 30 Aug 2002
Date of revision:
Handle: RePEc:wpa:wuwpfi:0207008

Note: Type of Document - postscript; prepared on MikTex; to print on postscript; pages: 41 ; figures: included. produced via dvips
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Web page: http://128.118.178.162

Related research

Keywords: currency options; skewness and kurtosis; Gram-Charlier expansions; implied volatility;

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References

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