Accouting for Biases in Black-Scholes

David Backus (), Silverio Foresi and Liuren Wu ()
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Silverio Foresi: Goldman Sachs

Finance from EconWPA

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.

Keywords: currency options; skewness and kurtosis; Gram-Charlier expansions; implied volatility (search for similar items in EconPapers)
JEL-codes: G12 G13 F31 C14 (search for similar items in EconPapers)
Date: 2002-08-30
Note: Type of Document - postscript; prepared on MikTex; to print on postscript; pages: 41 ; figures: included. produced via dvips
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpfi:0207008

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