Does Statistical Dependence Matter? Evidence from the USD/AUD

This study investigates the effect of volatility scaling on valuing financial assets by examining the long-term return properties of the spot USD/AUD. Tests are conducted for evidence of a scaling law in USD/AUD returns. The economic implications of dependence and non-normality of the distribution of returns are explored using the Garman and Kohlhagen modified Black–Scholes model for valuing foreign currency options. The results suggest that the USD/AUD does not conform to a stable distribution and that as a result of differential scaling laws, Garman and Kohlhagen option values using implied annual volatility will be consistently too high or too low.