Parameter estimation bias and volatility scaling in Blackââ"šÂ¬Ã¢â‚¬Å“Scholes option prices

When asset returns conform to a Gaussian distribution, the moments of the distribution over long return intervals may be estimated by scaling the moments of 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 investigates the return properties of the most important currencies traded in spot markets against the U.S. dollar: the Japanese yen, the British pound, and the Swiss franc during the period November 1983 to April 2004. The novelty of this paper is that the volatility properties of the series are tested utilising statistical procedures developed from fractal geometry, with the economic impact determined within an option-pricing framework.