Accounting for Biases in Black-Scholes
46 Pages Posted: 3 Sep 2004
Date Written: August 31, 2004
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 at-the-money options increases, on average, with maturity). We account for both using Gram-Charlier 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 Black-Scholes option prices decline with maturity.
Keywords: Currency options, skewness and kurtosis, Gram-Charlier expansions, implied volatility
JEL Classification: G12, G13, F31, C14
Suggested Citation: Suggested Citation