Volatility Scaling in Foreign Exchange Markets

Abstract

When distributions are non-Gaussian or display linear dependence it may not be appropriate to annualise the risk coefficient determined by the linear rescaling of the variance from other time intervals. This paper investigates the scaling relationships for daily spot foreign currency returns: the Deutsche mark-U.S. dollar (DMK/USD), the Swiss franc-USD (SWF/USD), the Japanese yen-USD (JPY/USD), and the English pound-USD (GBP/USD), from February 1985 to May 1998. We find that all four series were non-Gaussian and displayed similar scaling properties with the estimated variance, based upon a scaling at the square root of time, significantly underestimating the actual level of risk predicted from a normal distribution. The economic implications of these results were then established by estimating the premiums on a series of foreign currency options using a variation of a Black-Scholes model with varying strike prices. Based on a 180 day maturity, the results suggested that the inappropriate scaling of risk underestimated the price of call and put options for DMK/USD, SWF/USD and JPY/USD, but not for GBP/USD.

JEL Classification: F31, G15, C53