When asset returns are normally distributed the risk of an asset over a long return interval may be estimated by scaling the risk from shorter return intervals. While it is well known that asset returns are not normally distributed a key empirical question concerns the effect that scaling the volatility of dependent processes will have on the pricing of related financial assets. This study provides an insight into this issue by investigating the return properties of the most important currencies traded in spot markets against the U.S. dollar: the Deutsche mark, the Swiss franc, the Japanese yen, and the British pound, during the period from January 1985 to December 1998. The novelty of this paper is that the volatility properties of the series are tested utilizing statistical procedures developed from fractal geometry after adjusting for dependence in the series, with the economic impact determined within an option-pricing framework. The results demonstrate that scaling risk underestimates the actual level of risk for all four series investigated. However while the call and put premiums on Deutsche mark, Swiss franc and yen options are too low, those on the English pound are not. In our discussion of the possible sources of option under-pricing both conditional heteroskedasticity and underpricing bias by the Black-Scholes model have been considered. However, these factors were unable to account for the very high levels of underpricing reported. In conclusion, these results highlight the complex behaviour of financial asset returns and the inability of general pricing models to completely and accurately describe this behaviour.
