Scaling properties of foreign exchange volatility

in this paper, we investigate the scaling properties of foreign exchange vo latility. Our methodology is based on a wavelet multi-scaling approach whic h decomposes the variance of a time series and the covariance between two t ime series on a scale by scale basis through the application of a discrete wavelet transformation. It is shown that foreign exchange rate volatilities follow different scaling laws at different horizons. Particularly, there i s a smaller degree of persistence in intra-day volatility as compared to vo latility at one day and higher scales. Therefore, a common practice in the risk management industry to convert risk measures calculated at shorter hor izons into longer horizons through a global scaling parameter may not be ap propriate. This paper also demonstrates that correlation between the foreig n exchange volatilities is the lowest at the intra-day scales but exhibits a gradual increase up to a daily scare. The correlation coefficient stabili zes at scales one day and higher. Therefore, the benefit of currency divers ification is the greatest at the intra-day scales and diminishes gradually at higher scales (lower frequencies). The wavelet cross-correlation analysi s also indicates that the association between two volatilities is stronger at lower frequencies. (C) 2001 Elsevier Science B.V. All rights reserved.