Risk-neutralized at-the-money consistent historical distributions in currency options pricing

ABSTRACT This paper demonstrates the usefulness of risk-neutralized at-the-money consistent historical distributions in estimating currency option prices that exhibit a volatility smile and replicate the term structure of volatility. Implied volatility smiles are constructed for the British pound, Japanese yen, and Deutschmark (euro) for the period 1980–2000. Since these smiles are constructed only from historical data on the underlying asset, not option prices, market-implied volatilities may be compared to the estimates from the historical distribution in order to measure the relative richness or cheapness of quoted options. Prior models of currency price evolution embodying restrictive assumptions about the functional form of the errors are not necessary. Since currency prices are leptokurtotic, a kernel estimation procedure of the historical distribution is introduced to properly account for the effects of outliers.