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Scaling properties of foreign exchange volatility

Ramazan Gencay, Faruk Selcuk and Brandon Whitcher

Physica A: Statistical Mechanics and its Applications, 2001, vol. 289, issue 1, 249-266

Abstract: In this paper, we investigate the scaling properties of foreign exchange volatility. Our methodology is based on a wavelet multi-scaling approach which decomposes the variance of a time series and the covariance between two time 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 is a smaller degree of persistence in intra-day volatility as compared to volatility at one day and higher scales. Therefore, a common practice in the risk management industry to convert risk measures calculated at shorter horizons into longer horizons through a global scaling parameter may not be appropriate. This paper also demonstrates that correlation between the foreign exchange volatilities is the lowest at the intra-day scales but exhibits a gradual increase up to a daily scale. The correlation coefficient stabilizes at scales one day and higher. Therefore, the benefit of currency diversification is the greatest at the intra-day scales and diminishes gradually at higher scales (lower frequencies). The wavelet cross-correlation analysis also indicates that the association between two volatilities is stronger at lower frequencies.

Keywords: Foreign exchange volatility; Scaling; Wavelets; Multi-scaling (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1016/S0378-4371(00)00456-8

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Handle: RePEc:eee:phsmap:v:289:y:2001:i:1:p:249-266